Contentsfcaa/contfc_all_10vol.pdf · INVOLVING GENERALIZED FRACTIONAL CALCULUS ... Vol. 1, No 2 (1998) Contents ... Contents Om P. Agrawal A GENERAL SOLUTION FOR THE FOURTH-ORDER

ISSN 1311-0454 FCAA, Vol. 1, No 1 (1998)

Contents

Preface

D. Przeworska-RolewiczCARLEMAN OPERATORS IN COMMUTATIVE ALGEBRASWITH LOGARITHMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Bl. Sendov, P. MarinovBINARY EXPONENTIAL FRACTAL FUNCTIONS . . . . . . . . . . . . . . . . . 23

L. Galue, S. L. KallaSOME RECURRENCE RELATIONS FOR THE GENERALIZEDHYPERGEOMETRIC FUNCTIONS OF THE GAUSS TYPE . . . . . . . . 49

Yu. Luchko, R. GorenfloSCALE-INVARIANT SOLUTIONS OF A PARTIAL DIFFERENTIALEQUATION OF FRACTIONAL ORDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

V. S. Kiryakova, M. Saigo, H. M. SrivastavaSOME CRITERIA FOR UNIVALENCE OF ANALYTIC FUNCTIONSINVOLVING GENERALIZED FRACTIONAL CALCULUSOPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Information on International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . .105

Addresses of the EB Members

Order Form, Subscription Details

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ISSN 1311-0454 FCAA, Vol. 1, No 2 (1998)

Contents

G. G. Walter, A. I. ZayedMULTIRESOLUTION ANALYSIS WITH SAMPLING SUBSPACES 109

C. A. M. van Berkel, J. de GraafTHE FOURIER-JACOBI TRANSFORM OF ANALYTIC FUNCTIONSWHICH ARE (ALMOST) PERIODIC IN THE IMAGINARYDIRECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

A. A. Kilbas, B. Bonilla, M. Rivero, J. Rodriguez, J. TrujilloCOMPOSITIONS OF BESSEL TYPE INTEGRAL TRANSFORMWITH FRACTIONAL OPERATORS ON SPACES Fp,µ AND F ′

p,µ . . 135

P. RusevON THE ASYMPTOTICS OF THE WEBER-HERMITE FUNCTIONIN THE COMPLEX PLANE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

R. Gorenflo, F. MainardiRANDOM WALK MODELS FOR SPACE-FRACTIONALDIFFUSION PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

B. RubinFRACTIONAL CALCULUS AND WAVELET TRANSFORMSIN INTEGRAL GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

Information on International Meetings . . . . . . . . . . . . . . . . . . . . . 192, 220

Proceedings “TMSF, Varna’96” (Contents) . . . . . . . . . . . . . . . . . . . . 221

Addresses of the EB Members

Order Form, Subscription Details

3

ISSN 1311-0454 FCAA, Vol. 1, No 3 (1998)

Contents

S. SamkoA NEW APPROACH TO THE INVERSIONOF THE RIESZ POTENTIAL OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . 225

V. M. Almeida, J. RodrıguezAN ALGEBRAIC DERIVATIVE AND SOME OFITS APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

E. BazhlekovaTHE ABSTRACT CAUCHY PROBLEM FORTHE FRACTIONAL EVOLUTION EQUATION . . . . . . . . . . . . . . . . . . . . 255

M. L. Glasser, A. A. Al-JarrahSOME SONINE-GEGENBAUER INTEGRALS . . . . . . . . . . . . . . . . . . . . . 271

G. R. MillerSHIFT OPERATORS AND FRACTIONAL CALCULUS . . . . . . . . . . . . 279

S. B. Yakubovich, L. D. GusarevichON THE NON-CONVOLUTION TRANSFORMATION WITHTHE MACDONALD TYPE KERNEL FUNCTION . . . . . . . . . . . . . . . . . 297

Jae Ho ChoiUNIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTSINVOLVING A CERTAIN FRACTIONAL INTEGRAL OPERATORAND ITS PARTIAL SUMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

Information on International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . 319

Proceedings of International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . 321

Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

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ISSN 1311-0454 FCAA, Vol. 1, No 4 (1998)

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B. StankovicS-BOUNDED FOURIER HYPERFUNCTIONS . . . . . . . . . . . . . . . . . . . . . 327R. K. Raina, R. N. KaliaCHARACTERIZATIONS FOR SUBCLASSES OF ANALYTICFUNCTIONS CONNECTING LINEAR FRACTIONALCALCULUS OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334S. KempfleCAUSALITY CRITERIA FOR SOLUTIONS OFLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . 351I. A. Aliev, S. BayrakciON INVERSION OF B-ELLIPTIC POTENTIALS BYTHE METHOD OF BALAKRISHNAN-RUBIN . . . . . . . . . . . . . . . . . . . . . 365L. Boyadjiev, H.-J. DobnerON THE SOLUTION OF A FRACTIONALFREE ELECTRON LASER EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385N. Sudland, G. Baumann, T. F. NonnenmacherOPEN PROBLEM: WHO KNOWS ABOUT THE ℵ-FUNCTIONS ? 401O. Marichev, M. TrottTHE MATHEMATICAL FUNCTIONS OF MATHEMATICA(Announce for a POSTER) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403Djrbashian Memorial Conference (DMC98)(Erevan, Sept. 10-12, 1998; M. M. Djrabshian 1918-1994) . . . . . . . . . . . . 409Colloquium FRACTIONAL DIFFERENTIAL SYSTEMS(Paris, December 3-4, 1998; Information) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415Internat. Conference on Scientific Computations(Beirut, March 15-17, 1999; ICS99) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417Session on FUNCTION SPACES AND APPL-S(Fukuoka, August 16-21, 1999; at Internat. Congress ISAAC99) . . . . . 4193rd Internat. Workshop TMSF, AUBG’99(Blagoevgrad (Bulgaria), August 13-20, 1999) . . . . . . . . . . . . . . . . . . . . . . . 421Addresses of the EB Members, Order Form FCAA . . . . . . . . . . . 425Contents of Vol.1, No 1 - No 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

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Contents

A. Oustaloup, J. Sabatier, P. LanusseFROM FRACTAL ROBUSTNESS TO THE CRONE CONTROL . . . . 1A. DenisjukINTEGRAL GEOMETRY ON THE FAMILY OF SEMI-SPHERES . . 31B. RubinLp-PROPERTIES OF SOLUTIONS OF THE SINGULARHELMHOLTZ EQUATION IN THE HALF-SPACE . . . . . . . . . . . . . . . . . . 47S. SamkoSOME REMARKS ON THE AUTHOR’S PAPER “A NEW APPROACHTO THE INVERSION OF THE RIESZ POTENTIAL OPERATOR” 63N. Karapetiants, S. SamkoMULTI-DIMENSIONAL INTEGRAL OPERATORSWITH HOMOGENEOUS KERNELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67E. Moiseev, K. Skornik, W. KieratLIFE AND WORK OF PROF. A.P. PRUDNIKOV . . . . . . . . . . . . . . . . . . 97A. Kilbas, S. SamkoA.P. PRUDNIKOV: A NOTE IN MEMORIAM . . . . . . . . . . . . . . . . . . . . . . 107A. Carpinteri, F. Mainardi (Ed-s)FRACTALS AND FRACTIONAL CALCULUS INCONTINUUM MECHANICS (Annotation of a Proceedings) . . . . . . . . . 109I. Podlubny (Author)FRACTIONAL DIFFERENTIAL EQUATIONS:An Introduction to . . . (Annotation of a New Book) . . . . . . . . . . . . . . . . . . 113R. Hilfer (Editor)APPLICATIONS OF FRACTIONAL CALCULUS IN PHYSICS(Annotation of a New Volume) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Informations on International Meetings“TMSF,AUBG’99”, “AMADE’99”, “AART’99” . . . . . 123, 125, 127Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Contents of Vol.1 (1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

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Vu Kim TuanPALEY-WIENER-TYPE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135M.L. Glasser, M.E.H. IsmailA CURIOUS EXPRESSION FOR THE WEYLFRACTIONAL INTEGRAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145D. Przeworska-RolewiczISOMORPHISMS PRESERVING LEIBNIZ CONDITION . . . . . . . . . . . 149R. Gorenflo, Yu. Luchko, P.P. ZabrejkoON SOLVABILITY OF LINEAR FRACTIONAL DIFFERENTIALEQUATIONS IN BANACH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163N.K. Karapetiants, L.D. ShankishviliA SHORT PROOF OF HARDY-LITTLEWOOD-TYPETHEOREM FOR FRACTIONAL INTEGRALS INWEIGHTED HOLDER SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .177A.N. Karapetyants, E. Ramırez de ArellanoCHARACTERIZATION OF ANISOTROPIC LIZORKIN-TYPEMIXED NORM SPACES GENERATED BY DEGENERATEDIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193V.A. Nogin, S.G. SamkoSOME APPLICATIONS OF POTENTIALS ANDAPPROXIMATIVE INVERSE OPERATORS INMULTI-DIMENSIONAL FRACTIONAL CALCULUS . . . . . . . . . . . . . . . 205

Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

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N. VirchenkoON SOME GENERALIZATIONS OF THE FUNCTIONSOF HYPERGEOMETRIC TYPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233F. Levron, J. Sabatier, A. Oustaloup, L. HabsiegerFROM PARTIAL DIFFERENTIAL EQUATIONSOF PROPAGATIVE RECURSIVE SYSTEMSTO NON INTEGER DIFFERENTIATION . . . . . . . . . . . . . . . . . . . . . . . . . . 245I. AlievON THE BOCHNER-RIESZ SUMMABILITYAND RESTORATION OF µ-SMOOTH FUNCTIONSBY MEANS OF THEIR FOURIER TRANSFORMS . . . . . . . . . . . . . . . . . 265R.M. Peat, W.J. Spratt & A.C. McBrideSPACES OF SMOOTH FUNCTIONS ON R+ FORMELLIN MULTIPLIER TRANSFORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .277R.M. Peat, A.C. McBrideSPACES OF SMOOTH FUNCTIONS ON Rn

VIA SPHERICAL HARMONICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289K. DiethelmESTIMATION OF QUADRATURE ERRORS IN TERMSOF CAPUTO-TYPE FRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . 313N.G. Samko, S.G. SamkoON APPROXIMATIVE DEFINITIONOF FRACTIONAL DIFFERENTIATION . . . . . . . . . . . . . . . . . . . . . . . . . . . .329A.A. Kilbas, J.J. TrujilloON THE HANKEL-TYPE INTEGRAL TRANSFORMIN Lν,r-SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343International MeetingsVIII INTERNATIONAL M. CRAVCHUK CONFERENCE . . . . . . . . . . .354Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

8

ISSN 1311-0454 FCAA, Vol. 2, No 4 (1999)

Proc. of the 4th International Workshop

“TMSF,AUBG’99”, Part A

Contents

Preface

E. BazhlekovaPERTURBATION PROPERTIES FOR ABSTRACT EVOLUTIONEQUATIONS OF FRACTIONAL ORDER . . . . . . . . . . . . . . . . . . . . . . . . . . .359

L.T. DechevskyATOMIC DECOMPOSITION OF FUNCTION SPACES ANDFRACTIONAL INTEGRAL AND DIFFERENTIAL OPERATORS . . 367

R. Gorenflo, Yu. Luchko, F. MainardiANALYTICAL PROPERTIES AND APPLICATIONSOF THE WRIGHT FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

S. Kempfle, I. SchaeferFUNCTIONAL CALCULUS METHODVERSUS RIEMANN-LIOUVILLE APPROACH . . . . . . . . . . . . . . . . . . . . . 415

A.A. Kilbas, M. Saigo, A. BorovcoON THE LOMMEL-MAITLAND TRANSFORM IN Lν,r-SPACE . . . . 429

V. KiryakovaMULTIINDEX MITTAG-LEFFLER FUNCTIONS,RELATED GELFOND-LEONTIEV OPERATORSAND LAPLACE TYPE INTEGRAL TRANSFORMS . . . . . . . . . . . . . . . . 445

Yu. LuchkoOPERATIONAL METHOD IN FRACTIONAL CALCULUS . . . . . . . . .463

S.T. MinchevaON THE AUTOMORPHISMS OF L1 COMMUTINGWITH A GENERALIZED INTEGRATION OPERATOR . . . . . . . . . . . . 489

9

A.H. Al-Shammery, S.L. Kalla, H.G. KhajahA FRACTIONAL GENERALIZATIONOF THE FREE ELECTRON LASER EQUATION . . . . . . . . . . . . . . . . . . .501

K. SkornikMIKUSINSKI’S OPERATIONAL CALCULUSAND ITS APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509

N. VirchenkoON A GENERALIZED LAGUERRE’S FUNCTIONAND ITS APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529

M. ZahleFRACTIONAL INTEGRALS AND DERIVATIVESWITH RESPECT TO A MEASURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537

H.M. SrivastavaBook’s Review: FRACTIONAL DIFFERENTIAL EQUATIONSby I. Podlubny . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

Reports on International MeetingsAART (Sept. 21-25, 1999, Warsaw) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546

Reports on International MeetingsAMADE (Sept. 14-18, 1999, Minsk) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547

Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549


Participants in the “TMSF,AUBG’99” Workshop . . . . . . . . . . . . . 553

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ISSN 1311-0454 FCAA, Vol. 2, No 5 (1999)

Proc. of the 4th International Workshop

“TMSF,AUBG’99”, Part B

Contents

Preface

M.B. Abd-el-Malek, F.H. Michael, A.H. TwefickNONLINEAR GRAVITY WAVES OVERIRREGULAR BOTTOM VIA PERTURBATION METHOD . . . . . . . . . 555

F. Al-Sirehy, B. FisherTHE COMPOSITION OF THE FUNCTIONS |x|−λ AND |x|2r/λ . . . . 575

G.I. Balikov, I.P. DimitrovSOME NOTES ON ZAHARIUTA-VOGT’S CONDITIONS . . . . . . . . . . 583

G.I. Chobanov, I.H. DimovskiA TWO-VARIATE OPERATIONAL CALCULUSFOR BOUNDARY VALUE PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .591

J. Chung, S.-Y. Chung, D. Kim, H. KimTRIGONOMETRIC SERIES ANDALMOST PERIODIC GENERALIZED FUNCTIONS . . . . . . . . . . . . . . . 603

Soon-Yeong ChungA TEMPERATURE TRANSFORM ANDA BIHARMONIC ANALYSIS ON TEMPERATURES . . . . . . . . . . . . . . . 613

S.-Y. Chung, D. Kim, Y. YeomSTIELTJES MOMENT PROBLEMFOR GEL’FAND-LEONTIEV SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623

I.P. DimitrovABOUT OVERCONVERGENT FUNCTIONAL SERIES INTHE SPACE OF ANALYTIC FUNCTIONS IN THE UNIT DISK . . . 631

S.B. DomaMOMENTS OF INERTIA OF DEFORMED NUCLEI . . . . . . . . . . . . . . . 637

A.M. HamzehDESIGN CONSIDERATIONS AND COMPUTATIONALMETHODS FOR ESTIMATION OF RATIOS . . . . . . . . . . . . . . . . . . . . . . . 651

11

A. Kaminski, D. Perisic, S. PilipovicTHE CONVOLUTION AND CONVOLUTORS INGEL’FAND-SHILOV SPACES OF DISTRIBUTIONS . . . . . . . . . . . . . . . . 657

E. Malkowsky, E. SavasMATRIX TRANSFORMATIONS IN SOME SPACESOF ALMOST SUMMABLE AND BOUNDED SEQUENCES . . . . . . . . 669

M.I. MitrevaTAME EXTENSION OPERATORS FOR HERMITE’SINTERPOLATION PROBLEM ON ANALYTIC VARIETES . . . . . . . . 679

J. Paneva-KonovskaA TAUBER TYPE THEOREMFOR SERIES IN BESSEL FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683

P. RusevPERRON’S TYPE ASYMPTOTIC FORMULASFOR THE LAGUERRE POLYNOMIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689

M. Salameh, A.N. El-Kassar, R.E. Ghattas, B.S. MaddahTHE CONTINUOUS REVIEW INVENTORYMODEL, A MODIFIED APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699

M. SkwarczynskiON COMPLETENESS OF INFINITELYCONNECTED DOMAINS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711

T. StoyanovABOUT A PROBLEM OF OBRESHKOFF . . . . . . . . . . . . . . . . . . . . . . . . . . 717

N. TuneskiA NOTE ON SOME SIMPLE SUFFICIENT CONDITIONSFOR UNIVALENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721

V. VatchevTURAN QUADRATURES FOR FOURIER COEFFICIENTSAND POLYNOMIALS OF MINIMAL DEVIATION . . . . . . . . . . . . . . . . . 729



Participants in the “TMSF,AUBG’99” Workshop . . . . . . . . . . . . . 743

12ISSN 1311-0454 FCAA, Vol. 3, No 1 (2000)

Contents

Om P. AgrawalA GENERAL SOLUTION FOR THE FOURTH-ORDERFRACTIONAL DIFFUSION-WAVE EQUATION . . . . . . . . . . . . . . . . . . . . . 1A. MeskhiON THE BOUNDEDNESS AND COMPACTNESS OF BALLFRACTIONAL INTEGRAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . 13D. Przeworska-RolewiczNULLITY, DEFICIENCY AND COMMUTATORS OFLINEAR, LOGARITHMIC AND ANTILOGARITHMIC MAPPINGS 31W. WyssTHE FRACTIONAL BLACK-SCHOLES EQUATION . . . . . . . . . . . . . . . . 51R.B. Paris, G.V. LiakhovetskiASYMPTOTICS OF THE MULTIDIMENSIONALFAXEN INTEGRAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63R. Gorenflo, A. Iskenderov, Yu. LuchkoMAPPING BETWEEN SOLUTIONS OF FRACTIONALDIFFUSION-WAVE EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75V.A. Nogin, P.A. LuzhetskayaINVERSION AND DESCRIPTION OF THE RANGESOF MULTIPLIER OPERATORS OFSTRICHARTZ–PERAL–MIYACHI-TYPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Kluwer Acad. Publishers:ENCYCLOPAEDIA OF MATHEMATICS (Info and Reprinted Items) 97D. Przeworska-Rolewicz, ALGEBRAIC ANALYSIS . . . . . . . . . . . . . . . 100B. Rubin, CALDERON-TYPE REPRODUCING FORMULA . . . . . . .103

International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Contents of Vol. 1 and Vol. 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

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Contents

A.W. Niukkanen, V.I. Perevozchikov, V.A. LurieA GENERALIZATION OF A CLASSICAL RELATION BETWEENJν+n(z), Jν(z) and Jν−1(z) WITH COMMENTS ONTHE MODERN STATE AND TRENDS IN SPECIAL FUNCTIONS 119Nguyen Minh Chuong, Ta Ngoc TriTHE INTEGRAL WAVELET TRANSFORM IN Lp(Rn), 1 ≤ p ≤ ∞ 133A.N. Karapetyants, E. Ramırez de ArellanoON THE INVERSION OF POTENTIAL TYPE OPERATORSWITH KERNELS HAVING SINGULARITIES ON A SPHERE . . . . . 141L. Galue, I. Ali, S.L. KallaAN EXTENSION OF THE LAGUERRE POLYNOMIALSAND ASSOCIATED ORTHONORMAL FUNCTIONS . . . . . . . . . . . . . . 161U. SkornikA REMARK ON ELEMENTS OF D′

Lq(R) ASBOUNDARY VALUES OF HOLOMORPHIC FUNCTIONS . . . . . . . . 173B. RubinGENERALIZED MINKOWSKI-FUNK TRANSFORMS AND SMALLDENOMINATORS ON THE SPHERE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

New Book from World Scientific Publ.:PARTIAL DIFFERENTIAL EQUATIONS, An Introduction withMathematica and Maple, by I.P. Stavroulakis, S. Tersian . . . . . . . . . . . . 205Old Book from Longman 7→ CRC Press:GENERALIZED FRACTIONAL CALCULUS AND APPLICATIONS,by V. Kiryakova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

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E.G. BazhlekovaSUBORDINATION PRINCIPLE FOR FRACTIONALEVOLUTION EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213B. M. Vinagre, I. Podlubny, A. Hernandez, V. FeliuSOME APPROXIMATIONSOF FRACTIONAL ORDER OPERATORSUSED IN CONTROL THEORY AND APPLICATIONS . . . . . . . . . . . . 231R. Gorenflo, Yu.F. Luchko, S.R. UmarovON THE CAUCHY AND MULTI-POINT PROBLEMSFOR PARTIAL PSEUDO-DIFFERENTIAL EQUATIONSOF FRACTIONAL ORDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249D. Przeworska-RolewiczSPECIAL FUNCTIONS AS ANTILOGARITHMSOF SECOND ORDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277N.M. Atakishiyev, M.K. AtakishiyevaON A SIMPLE INTEGRAL REPRESENTATIONOF THE CONTINUOUS q-HERMITE POLYNOMIALS . . . . . . . . . . . . 297F. Al-Musallam, Vu Kim TuanA CLASS OF CONVOLUTION TRANSFORMATIONS . . . . . . . . . . . . 303Open Problem: ARITHMETICAL PROPERTIES OFGEGENBAUER POLYNOMIALS . . . , by B. Rubin . . . . . . . . . . . . . . . . 315Corrigenda: LETTER, by S. Samko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317Corrigenda: CORRECTIONS to paper: “A two-variate operational . . . ”,FCAA 2, No 5 (1999), 591-601, by G.I. Chobanov, I.H. Dimovski . . . . 318

Anniversary: 60th ANNIVERSARY of Professor H.M. Srivastava . 319

Meetings: 3rd Internat. ISAAC Congress (Berlin, 2001) . . . . . . . . . . . . . 327Meetings: Internat. Conf. ”AMADE-2001” (Minsk) . . . . . . . . . . . . . . . . . 333Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

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Anniversary: 70th ANNIVERSARY of Professor R. GORENFLONew Website: FRACALMOLetters by V. Kiryakova, A. Kilbas and S. Samko, O. Marichev . . . . . . 339CV and List of Publications of R. Gorenflo . . . . . . . . . . . . . . . . . . . . . . . . . . 343

Vu Kim Tuan, Dinh Thanh DucAUTOMATIC EVALUATION OF AN ABSCISSA OFCONVERGENCE FOR INVERSE LAPLACE TRANSFORM . . . . . . 353I. PodlubnyMATRIX APPROACH TO DISCRETE FRACTIONAL CALCULUS 359S. Kempfle, I. SchaferFRACTIONAL DIFFERENTIAL EQUATIONSAND INITIAL CONDITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387S.G. Samko, B.G. VakulovON EQUIVALENT NORMS IN FRACTIONAL ORDERFUNCTION SPACES OF CONTINUOUS FUNCTIONSON THE UNIT SPHERE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401B. RubinFRACTIONAL DIFFERENTIATION ANDSPHERICAL RADON TRANSFORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435A.A. Kilbas, S.V. DemiankoSOLUTION OF MULTI-DIMENSIONAL ABEL-TYPE INTEGRALEQUATIONS WITH POWER-LOGARITHMIC KERNELS . . . . . . . . . 439R. Gorenflo, Yu.F. Luchko, S.R. UmarovON SOME BOUNDARY VALUE PROBLEMSFOR PSEUDO-DIFFERENTIAL EQUATIONS WITHBOUNDARY OPERATORS OF FRACTIONAL ORDER . . . . . . . . . . . 453

In Memoriam: Prof. IAN N. SNEDDON (08.12.1919-04.11.2000) . . 469Notes by V. Kiryakova, A. McBride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471Meetings: “OPSFA”, Roma, June 18-22, 2001 . . . . . . . . . . . . . . . . . . . . . 438Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477

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V. Kokilashvili, A. MeskhiFRACTIONAL INTEGRALS ON MEASURE SPACES . . . . . . . . . . . . . . 1P. Mikusinski, M. MorimotoBOEHMIANS ON THE SPHERE AND THEIR SPHERICALHARMONIC EXPANSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25G.D. Handley, J.J. Koliha, J. PecaricHILBERT-PACHPATTE TYPE INTEGRAL INEQUALITIESFOR FRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37J. A. Tenreiro MachadoDISCRETE-TIME FRACTIONAL-ORDER CONTROLLERS . . . . . . . 47A.P. Chegolin, V.A. NoginON THE L - CHARACTERISTIC OF SOME MULTIPLIEROPERATORS WITH OSCILLATING SYMBOLSIN THE NON-ELLIPTIC CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67F.M. Hafez, A.M.A. El-Sayed, M.A. El-TawilON A STOCHASTIC FRACTIONAL CALCULUS . . . . . . . . . . . . . . . . . . 81S.L. Kalla, B.N. Al-SaqabiFURTHER RESULTS ON A UNIFIED FORMOF GAMMA-TYPE DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91B.G. Vakulov, N.K. Karapetiants, L.D. ShankishviliSPHERICAL HYPERSINGULAR OPERATORSOF IMAGINARY ORDER AND THEIR MULTIPLIERS . . . . . . . . . . . . 101

Anniversary: 60th ANNIVERSARY of Professor S. SAMKOLetters by the Editor, N. Karapetiants and A. Kilbas, B. Rubin . . . . . . 113CV and List of Publications of S. Samko . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Meetings: “Constructive Function Theory 2002”, Varna, Bulgaria . . 36Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

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Tae Sik Kim, Seunghwan KimRELATIONS BETWEEN DIMENSIONS ANDDIFFERENTIABILITY OF CURVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Nguyen Minh Chuong, Bui Kien CuongGALERKIN-WAVELET APPROXIMATION FOR A CLASSOF PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS . . . . . . . . . . 143F. Mainardi, Yu. Luchko, G. PagniniTHE FUNDAMENTAL SOLUTION OFTHE SPACE-TIME FRACTIONAL DIFFUSION EQUATION . . . . . . 153D. Przeworska-RolewiczRIEMANN-HILBERT TYPE PROBLEMS WITH INVOLUTIONSIN LEIBNIZ ALGEBRAS WITH LOGARITHMS . . . . . . . . . . . . . . . . . . . 193G.F. RoachWAVE SCATTERINGBY TIME DEPENDENT PERTURBATIONS . . . . . . . . . . . . . . . . . . . . . . 209I. Dimovski, K. SkornikMEAN-PERIODIC OPERATIONAL CALCULI. SINGULAR CASES . . .237I. Dimovski, A. Kaminski, S. MinchevaTHE COMMUTANT OF AN INTEGRATION OPERATORWITH MULTIPOINT FUNCTIONAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

Anniversary: 70th ANNIVERSARY ofProfessor Danuta PRZEWORSKA-ROLEWICZLetters by the Editor and K. Skornik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255CV and List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

Meetings: “Analytical Methods of Analysis and Differential Equations”(AMADE-2001), Minsk, Belarus, February 15-19, 2001 . . . . . . . . . . . . . . 267Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

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M. M. Wyss, W. WyssEVOLUTION, ITS FRACTIONAL EXTENSIONAND GENERALIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273K. M. Kolwankar, J. Levy VehelMEASURING FUNCTIONS SMOOTHNESS WITHLOCAL FRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285M. Aslam Chaudhry, S. M. ZubairEXTENDED GAMMA AND DIGAMMA FUNCTIONS . . . . . . . . . . . . 303S. R. Umarov, E. M. SaydamatovON THE SPECTRUM OF GENERALPSEUDO-DIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . 327V. A. Nogin, D. N. KarausevON THE L-CHARACTERISTIC OF SOME POTENTIAL -TYPE OPERATORS WITH RADIAL KERNELS,HAVING SINGULARITIES ON A SPHERE . . . . . . . . . . . . . . . . . . . . . . . . 343Jae Ho Choi, Yong Chan Kim, S. OwaFRACTIONAL CALCULUS OPERATOR AND ITSAPPLICATIONS IN THE UNIVALENT FUNCTIONS . . . . . . . . . . . . . 367L. Boyadjiev, S. L. KallaSERIES REPRESENTATIONS OF ANALYTIC FUNCTIONSAND APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

Anniversary: 70th ANNIVERSARY of Professor Peter RUSEV . . . . 409

New Books: by H.M. Srivastava and J. Choi . . . . . . . . . . . . . . . . . . . . . . 302by M Aslam Chaudhry and S.M Zubair . . . . . . . . . . . . . . 325

Addresses of EB Members, Order Form, Subscriptions . . . . . . 417

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M. CaputoDISTRIBUTED ORDER DIFFERENTIAL EQUATIONSMODELLING DIELECTRIC INDUCTION AND DIFFUSION . . . . . 421H. Mejjaoli, Kh. TrimecheHARMONIC ANALYSIS ASSOCIATED WITHTHE DUNKL-BESSEL LAPLACE OPERATORAND A MEAN VALUE PROPERTY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443B. Baeumer, M.M. MeerschaertSTOCHASTIC SOLUTIONS FOR FRACTIONALCAUCHY PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481B. Stankovic, T.M. AtanackovicON A MODEL OF A VISCOELASTIC ROD . . . . . . . . . . . . . . . . . . . . . . . 501S. Samko, M. YakhshiboevON A CLASS OF IDENTITY APPROXIMATIONOPERATORS OF A NON-CONVOLUTION TYPE . . . . . . . . . . . . . . . . 523K. Diethelm, N.J. FordNUMERICAL SOLUTION METHODS FORDISTRIBUTED ORDER DIFFERENTIAL EQUATIONS . . . . . . . . . . 531Yu.A. BrychkovA GENERALIZATION OF THE COOKE’S DUPLICATIONFORMULAS FOR BESSEL FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 543In Memoriam: Prof. E.R. LOVE (31.03.1912-7.08.2001) . . . . . . . . . . . 549Obituary by J.F. Clark, Note by Editor . . . . . . . . . . . . . . . . . . . . . . . . 550, 551A note in memoriam by A. Kilbas, S. Samko . . . . . . . . . . . . . . . . . . . . . . . . 552

Books: by N. Virchenko, I. Fedotova, “Generalized Associated ... ” 555by U. Trottenberg, C.W. Oosterlee, A. Schuller, “Multigrid” 557

International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558, 559, 562, 563


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A. Jouini, K. TrimecheGENERALIZED WAVELET PACKETS AND APPLICATIONTO THE INVERSION OF THE J.L. LIONSTRANSMUTATION OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

M.M. Meerschaert, H.-P. SchefflerSEMISTABLE LEVY MOTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

L. de Rosa, A. de la TorreON CONDITIONS FOR THE BOUNDEDNESSOF THE WEYL FRACTIONAL INTEGRALIN THE CASE 1 < q ≤ p < ∞ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55G. Dattoli, P.E. Ricci, C. CesaranoDIFFERENTIAL EQUATIONS FORAPPELL TYPE POLYNOMIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

N. Jacob, A. M. KragelohFELLER SEMIGROUPS ON C∞(Rn × T 1) GENERATED BYWEYL FRACTIONAL DERIVATIVESAND PSEUDO-DIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . . . . 77

Book’s Review, by V. A. Nogin, for:HYPERSINGULAR INTEGRALS AND THEIRAPPLICATIONS, by Stefan G. Samko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Letter to Editor, by S. G. Samko:Prof. N. KARAPETIANTS’s 60th BIRTHDAY . . . . . . . . . . . . . . . . . . . . . . 123


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D.N. KarasevLp → Lq - ESTIMATES FOR SOME POTENTIAL-TYPEOPERATORS WITH OSCILLATING KERNELS . . . . . . . . . . . . . . . . . . . 131A.A. Rousan, E. Malkawi, E.M. Rabei, H. WidyanAPPLICATIONS OF FRACTIONAL CALCULUSTO GRAVITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155P.K. Banerji, L. Debnath, G.M. ShenanAPPLICATION OF FRACTIONAL DERIVATIVEOPERATORS TO THE MAPPING PROPERTIESOF ANALYTIC FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169V. Karunakaran, R. RoopkumarULTRA BOEHMIANSAND THEIR FOURIER TRANSFORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 181D. Przeworska-RolewiczBINOMIALS FORMULAEIN COMMUTATIVE LEIBNIZ ALGEBRAS WITH LOGARITHMS 195A.A. Kilbas, E.K. SchetnikovichGENERALIZED HANKEL-TYPE INTEGRAL TRANSFORMON Lν,r-SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Archives: B. L. J. BraaksmaIN MEMORIAM C. S. MEIJER (originally publ. in“Nieuw Archief voor Wiskunde (3)”, XXIII (1975), 95-104) . . . . . . . . . . 227

Letter to Editor, by S. G. Samko:CONGRATULATIONS TO VIRGINIA KIRYAKOVAON HER 5Oth ANNIVERSARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245, 249


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V. Kokilashvili, A. MeskhiWEIGHT INEQUALITIES FOR ONE–SIDED POTENTIALSFOR CRITICAL WEIGHTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

H. Irmak, G. Tinaztepe, Y.C. Kim, J.H. ChoiCERTAIN CLASSES AND INEQUALITIES INVOLVINGFRACTIONAL CALCULUSAND MULTIVALENT FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

A. YakubovFRACTIONAL TYPE INTEGRATION OPERATORS INWEIGHTED GENERALIZED HOLDER SPACES . . . . . . . . . . . . . . . . . . 275

N. K. KarapetiantsON BEHAVIOUR OF THE NORMS OF FRACTIONALINTEGRALS OF LARGE ORDERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

N.E. Cho, S.Y. Woo, S. OwaUNIFORM CONVEXITY PROPERTIESFOR HYPERGEOMETRIC FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 303

D.N. Karasev, V.A. NoginDESCRIPTION OF THE RANGES OF SOMEPOTENTIAL-TYPE OPERATORS WITH OSCILLATINGKERNELS IN THE NON-ELLIPTIC CASE . . . . . . . . . . . . . . . . . . . . . . . . 315

International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266, 314

Addresses of EB Members, Order Form, Subscriptions 351 - 354

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Anniversary: 60th ANNIVERSARY of Professor F. MAINARDICONGRATULATIONS, LIST OF PUBLICATIONS . . . . . . . . . . . . . . . . 357I. PodlubnyGEOMETRIC AND PHYSICAL INTERPRETATIONOF FRACTIONAL INTEGRATION ANDFRACTIONAL DIFFERENTIATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367Vu Kim Tuan, Dinh Thanh DucA NEW REAL INVERSION FORMULA OF THELAPLACE TRANSFORM AND ITS CONVERGENCE RATE . . . . . . 387N. Jacob, A. M. KragelohTHE CAPUTO DERIVATIVE, FELLER SEMIGROUPS,AND THE FRACTIONAL POWER OFTHE FIRST ORDER DERIVATIVE ON C∞(R+

0 ) . . . . . . . . . . . . . . . . . . 395S. Kempfle, I. Schafer, H. BeyerFUNCTIONAL CALCULUS AND A LINKTO FRACTIONAL CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411E. BazhlekovaSTRICT Lp SOLUTIONSFOR FRACTIONAL EVOLUTION EQUATIONS . . . . . . . . . . . . . . . . . . 427A.A. Kilbas, M. Saigo, J.J. TrujilloON THE GENERALIZED WRIGHT FUNCTION . . . . . . . . . . . . . . . . . . 437O. V. Doubrovina, S. V. RogosinON LINEAR AND NONLINEAR INTEGRAL EQUATIONSON FINITE INTERVALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461H.M. SrivastavaSOME FAMILIES OF MULTIVARIABLE BIORTHOGONALPOLYNOMIALS AND ASSOCIATEDGENERATING FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479R. Gorenflo, J. Loutchko, Yu. LuchkoCOMPUTATION OF THE MITTAG-LEFFLER FUNCTIONEα,β(z) AND ITS DERIVATIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491

International Meeting: AMADE-2003 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519Addresses of EB Members, Order Form, Subscriptions 521 - 524

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A. Oustaloup, V. Pommier, P. LanusseDESIGN OF A FRACTIONAL CONTROLUSING PERFORMANCE CONTOURS.APPLICATION TO AN ELECTROMECHANICAL SYSTEM . . . . . . . 1B. RubinNOTES ON RADON TRANSFORMSIN INTEGRAL GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25J. A. Tenreiro MachadoA PROBABILISTIC INTERPRETATION OFTHE FRACTIONAL-ORDER DIFFERENTIATION . . . . . . . . . . . . . . . . . 73P. RusevA NOTE ON JONQUIERE POLYNOMOALS . . . . . . . . . . . . . . . . . . . . . . . 81Yu. V. Vasil’evMODIFIED WHITTAKER TRANSFORMON Lν,r-SPACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Corrections: to Figure 4 in:“GEOMETRIC AND PHYSICAL INTERPRETATION . . . ”,FCAA 5, No 4 (2002), 367-386, by I. Podlubny . . . . . . . . . . . . . . . . . . . . . . 109Corrections: to paper“COMPUTATION OF THE MITTAG-LEFFLER FUNCTION . . . ”,FCAA 5, No 4 (2002), 491-518,by R. Gorenflo, J. Loutchko, Y. Luchko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Addresses of EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

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L. DebnathFRACTIONAL INTEGRAL AND FRACTIONALDIFFERENTIAL EQUATIONS IN FLUID MECHANICS . . . . . . . . . 119

V. V. Anh, R. McVinishCOMPLETELY MONOTONE PROPERTYOF FRACTIONAL GREEN FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 157

F. Al-MusallamTHE RANGE OF FINITE INTEGRAL TRANSFORMSARISING FROM n-th ORDER SINGULARSELF-ADJOINT DIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . 175

L. Beghin, E. OrsingherTHE TELEGRAPH PROCESS STOPPEDAT STABLE-DISTRIBUTED TIMES AND ITS CONNECTIONWITH THE FRACTIONAL TELEGRAPH EQUATION . . . . . . . . . . . . 187

I. Petras, L. DorcakFRACTIONAL-ORDER CONTROL SYSTEMS:MODELLING AND SIMULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

Addresses of EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

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S. G. Samko, R. P. CardosoSONINE INTEGRAL EQUATIONSOF THE FIRST KIND IN Lp(0, b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V. Yu. GoncharDISTRIBUTED ORDER TIME FRACTIONALDIFFUSION EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

H.M. Srivastava, A.K. Mishra, M.K. DasA CLASS OF PARABOLIC STARLIKE FUNCTIONSDEFINED BY MEANS OF A CERTAINFRACTIONAL DERIVATIVE OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . 281

J. Paneva-KonovskaCOMPLETE SYSTEMS OF BESSEL FUNCTIONS OFFIRST KIND IN SPACES OF HOLOMORPHIC FUNCTIONS . . . . . 299

A. AlmeidaINVERSION OF THE RIESZ POTENTIAL OPERATORON LEBESGUE SPACES WITH VARIABLE EXPONENT . . . . . . . . . 311

International MeetingsSecond Announcement and Call for Papers forFirst IFAC Workshop on “FDA’04, Bordeaux, France” . . . . . . . . . . . . . . 329


27ISSN 1311-0454 FCAA, Vol. 6, No 4 (2003)

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Anniversary: 75th ANNIVERSARY of Professor P.L. BUTZER . . . 333Anniversary: 70th ANNIVERSARY of Professor G.F. ROACH . . . . 341S. SamkoHARDY INEQUALITY INTHE GENERALIZED LEBESGUE SPACES . . . . . . . . . . . . . . . . . . . . . . . 355A.A. Kilbas, M. Rivero, J.J. TrujilloEXISTENCE AND UNIQUENESS THEOREMS FORDIFFERENTIAL EQUATIONS OF FRACTIONAL ORDERIN WEIGHTED SPACES OF CONTINUOUS FUNCTIONS . . . . . . . . 363D. Przeworska-RolewiczRICCATI TYPE EQUATIONS INLEIBNIZ ALGEBRAS WITH LOGARITHMS . . . . . . . . . . . . . . . . . . . . . . 401S. SamkoHARDY-LITTLEWOOD-STEIN-WEISS INEQUALITY INTHE LEBESGUE SPACES WITH VARIABLE EXPONENT . . . . . . . 421F. Mainardi, G. Pagnini, R. GorenfloMELLIN TRANSFORM AND SUBORDINATION LAWSIN FRACTIONAL DIFFUSION PROCESSES . . . . . . . . . . . . . . . . . . . . . . 441V. Kokilashvili, A. MeskhiON A TRACE INEQUALITY FOR ONE-SIDED POTENTIALSWITH MULTIPLE KERNELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461V.B. Shakhmurov, A.I. ZayedFRACTIONAL WIGNER DISTRIBUTIONAND AMBIGUITY FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473P. RusevCORRIGENDUM to my paper in: “FCAA”, vol. 6, No 1 (2003)“A NOTE ON JONQUIERE POLYNOMOALS” . . . . . . . . . . . . . . . . . . . . 491Addresses of EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

28ISSN 1311-0454 FCAA, Vol. 7, No 1 (2004)

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A.A. Al-JarrahLp-ESTIMATES OF ROUGH INTEGRAL OPERATORSWITH KERNELS INVOLVING BESSEL FUNCTIONS . . . . . . . . . . . . . . 1B. Stankovic, T.M. AtanackovicON AN INEQUALITY ARISING IN FRACTIONALOSCILLATOR THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11L. Debnath, D.D. BhattaSOLUTIONS TO FEW LINEAR FRACTIONALINHOMOGENEOUS PARTIAL DIFFERENTIAL EQUATIONSIN FLUID MECHANICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21N.B. Salem, A.O.A. SalemSOBOLEV TYPE SPACES ASSOCIATEDWITH THE JACOBI-DUNKL OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . 37M.M. Meerschaert, J. Mortensen, H.-P. SchefflerVECTOR GRUNWALD FORMULA FORFRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Report on 3rd International Conference”Analytic Methods of Analysis and Differential Equations”(AMADE’ 2003) – Minsk, Belarus, Sept. 4-9, 2003 . . . . . . . . . . . . . . . . . . . 83

Report on 4th International Symposium‘Transform Methods & Special Functions, Borovets’ 2003”(TMSF, Borovets’ 2003) – Borovets, Bulgaria, Sept. 15-21, 2003 . . . . . 86

Contents of “FCAA”Volume 1 (1998) – Volume 6 (2003) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89


29ISSN 1311-0454 FCAA, Vol. 7, No 2 (2004)

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R.S. Barbosa, J.A.Tenreiro Machado, I.M. FerreiraPID CONTROLLER TUNINGUSING FRACTIONAL CALCULUS CONCEPTS . . . . . . . . . . . . . . . . . . 119R.K. Saxena, T.F. NonnenmacherAPPLICATION OF THE H-FUNCTION IN MARKOVIANAND NON-MARKOVIAN CHAIN MODELS . . . . . . . . . . . . . . . . . . . . . . . 135V. KnopovaON SOME OPERATORS WITH COMPLEX-VALUEDCONTINUOUS NEGATIVE DEFINITE SYMBOLWHICH ARE GENERATORSOF Lp-SUB-MARKOVIAN SEMIGROUPS . . . . . . . . . . . . . . . . . . . . . . . . . 149G. Dattoli, M. Migliorati, H.M. SrivastavaA CLASS OF BESSEL SUMMATION FORMULASAND ASSOCIATED OPERATIONAL METHODS . . . . . . . . . . . . . . . . . 169A.I. KheyfitsCLOSED-FORM REPRESENTATIONSOF THE LAMBERT W FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177K. Diethelm, M. WeilbeerA NUMERICAL APPROACH FOR JOULIN’S MODELOF A POINT SOURCE INITIATED FLAME . . . . . . . . . . . . . . . . . . . . . . 191M.A. Betilgiriev, D.N. Karasev, V.A. NoginLp − Lq - ESTIMATES FOR SOME FRACTIONAL TYPEOPERATORS WITH OSCILLATING KERNELS . . . . . . . . . . . . . . . . . . 213


30ISSN 1311-0454 FCAA, Vol. 7, No 3 (2004)

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Anniversary: 70th ANNIVERSARY of Professor Ivan DIMOVSKI 245

Y. Ben Nakhi and S.L. KallaON SOME MIXTURE DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 261

D. Przeworska-RolewiczPOWERS AND LOGARITHMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

A.A. Kilbas, S.A. MarzanCAUCHY PROBLEM FOR DIFFERENTIAL EQUATIONWITH CAPUTO DERIVATIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

Nguyen Xuan Thao, Vu Kim Tuan, Nguyen Minh KhoaA GENERALIZED CONVOLUTION WITHA WEIGHT FUNCTION FOR THE FOURIERCOSINE AND SINE TRANSFORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

Yu. LuchkoOPERATIONAL RULES FOR A MIXED OPERATOROF THE ERDELYI-KOBER TYPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339

T. M. Atanackovic, B. StankovicAN EXPANSION FORMULA FOR FRACTIONALDERIVATIVES AND ITS APPLICATION . . . . . . . . . . . . . . . . . . . . . . . . . 365

31ISSN 1311-0454 FCAA, Vol. 7, No 4 (2004)

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M. Jelassi, L.T. RachdiON THE RANGE OF THE FOURIER TRANSFORMASSOCIATED WITH THE SPHERICAL MEAN OPERATOR . . . . . 379J. A. Tenreiro Machado, I. S. JesusSUGGESTION FROM THE PAST? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403N. Sudland, G. BaumannON THE MELLIN TRANSFORMS OF DIRAC’SDELTA FUNCTION, THE HAUSDORFF DIMENSIONFUNCTION, AND THE THEOREM BY MELLIN . . . . . . . . . . . . . . . . . 409M. Assal, H. Ben AbdallahCAUCHY PROBLEM FOR DIFFERENTIAL EQUATIONWITH CAPUTO DERIVATIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .N.K. Karapetyants †, N. SamkoWEIGHTED THEOREMS ON FRACTIONAL INTEGRALSIN THE GENERALIZED HOLDER SPACESVIA INDICES mω AND Mω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .M. D. Ortigueira, F. CoitoFROM DIFFERENCES TO DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . .

In Memoriam: Prof. John Boersma (1937 – 2004)OBITUARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

In Memoriam: Prof. Nikolai Karapetyants (1942 – 2005)OBITUARY by Ya. Erusalimskii, A. Kilbas, V. Kokilashvili, V.Rabinovich, V. Kokilashvili, S. Samko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Meetings: AMADE’2006, Second Announcement . . . . . . . . . . . . . . . . . . . . . .

Addresses of EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

32ISSN 1311-0454 FCAA, Vol. 8, No 1 (2005)

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Anniversary: 80th ANNIVERSARY of Acad. B. STANKOVIC,Part 1 (pp. 1 - 66) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

F. Mainardi, R. Gorenflo, A. VivoliRENEWAL PROCESSESOF MITTAG-LEFFLER AND WRIGHT TYPE . . . . . . . . . . . . . . . . . . . . . . 7S. SamkoBEST CONSTANT IN THE WEIGHTED HARDY INEQUALITY:THE SPATIAL AND SPHERICAL VERSION . . . . . . . . . . . . . . . . . . . . . . . 39I. Schafer, S. Kempfle, B. NolteLINEAR FRACTIONAL PDE,UNIQUENESS OF GLOBAL SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 53P. RusevA NOTE ON A CLASSICAL GENERATING FUNCTIONFOR THE JACOBI POLYNOMIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

New Book: by Anatolii A. Kilbas and Megumi Saigo,“H - TRANSFORMS. Theory and Applications”, CRC Press, 2004 . . . 67New Book: by George M. Zaslavsky, “HamiltonianChaos and Fractional Dynamics”, Oxford Univ. Press, 2004 . . . . . . . . . . 69Meetings: “International Symposium on Analytic FunctionTheory, Fractional Calculus and Their Applications”, in honourof 65th Birth Anniversary of Prof. H.M. Srivastava, August 2005 . . . . . 71Corrigenda: Correction to name of R.K. Saxena, in paper:“Application of the H-function in . . . ” in FCAA 7, No 2 (2004),133-148, by R. K. Saxena and Theo F. Nonnenmacher . . . . . . . . . . . . . . . . 72

S. Umarov, R. GorenfloON MULTI-DIMENSIONAL RANDOM WALK MODELSAPPROXIMATING SYMMETRIC SPACE-FRACTIONALDIFFUSION PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

33ISSN 1311-0454 FCAA, Vol. 8, No 2 (2005)

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Anniversary: 80th ANNIVERSARY of Acad. B. STANKOVIC,Part 2 (Collection of papers by Guest-Editor S. Samko) . . . . . . . . . . . . . . 89

N. Jacob, V. KnopovaFRACTIONAL DERIVATIVES AND FRACTIONAL POWERSAS TOOLS IN UNDERSTANDING WENTZELL BOUNDARYVALUE PROBLEMS FOR PSEUDO-DIFFERENTIAL OPERATORSGENERATING MARKOV PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . 91A.A. KilbasFRACTIONAL CALCULUS OF THE GENERALIZEDWRIGHT FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113H.J. Seybold, R. HilferNUMERICAL RESULTS FOR THE GENERALIZEDMITTAG-LEFFLER FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127R.K. Saxena, M. SaigoCERTAIN PROPERTIES OF FRACTIONAL CALCULUSOPERATORS ASSOCIATED WITHGENERALIZED MITTAG-LEFFLER FUNCTION . . . . . . . . . . . . . . . . . 141A.N. Karapetyants, D.N. Karasev, V.A. NoginLP → LQ-ESTIMATES FOR THE FRACTIONALACOUSTIC POTENTIALS ANDSOME RELATED OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155R. Gorenflo, E. A. Abdel-RehimDISCRETE MODELS OF TIME-FRACTIONAL DIFFUSIONIN A POTENTIAL WELL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173C. Martınez, M. Sanz, A. RedondoFRACTIONAL POWERS OF ALMOSTNON-NEGATIVE OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201


34ISSN 1311-0454 FCAA, Vol. 8, No 3 (2005)

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A. Al-SalmanROUGH MAXIMAL OSCILLATORY SINGULARINTEGRAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

M. Bezzarga, Kh. KefiON A SINGULAR VALUE PROBLEM FORTHE FRACTIONAL LAPLACIAN ON THE EXTERIOROF THE UNIT BALL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

J.D. Griffiths, G.M. Leonenko, J.E. WilliamsGENERALIZATION OF THE MODIFIED BESSELFUNCTION AND ITS GENERATING FUNCTION . . . . . . . . . . . . . . . . 267

A. KhelifiASYMPTOTIC PROPERTY OF EIGENVALUESAND EIGENFUNCTIONS OF THE LAPLACE OPERATORIN DOMAIN WITH A PERTURBED BOUNDARY . . . . . . . . . . . . . . . . 277

L. KamounAN LP − LQ−VERSION OF MORGAN’S THEOREMASSOCIATED WITHPARTIAL DIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . 299

S.L. Kalla, R.K. Yadav, S.D. PurohitON THE RIEMANN-LIOUVILLE FRACTIONALq-INTEGRAL OPERATOR INVOLVING A BASICANALOGUE OF FOX H-FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

M. Ilic, F. Liu, I. Turner, V. AnhNUMERICAL APPROXIMATION OFA FRACTIONAL-IN-SPACE DIFFUSION EQUATION, I . . . . . . . . . . 323

35ISSN 1311-0454 FCAA, Vol. 8, No 4 (2005)

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H. Wysocki, M. ZellmaAN ABSTRACT SECOND KIND FREDHOLMINTEGRAL EQUATION WITH DEGENERATED KERNEL . . . . . . . 343P.J. MianaCONVOLUTION PRODUCTS IN L1(R+),INTEGRAL TRANSFORMS AND FRACTIONAL CALCULUS . . . . 361B. Baeumer, S. Kurita, M.M. MeerschaertINHOMOGENEOUS FRACTIONALDIFFUSION EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

Anniversary: 65th ANNIVERSARY of Prof. H.M. Srivastava . . . . . . 387

H. Rafeiro, S. SamkoON MULTIDIMENSIONAL ANALOGUE OF MARCHAUDFORMULA FOR FRACTIONAL RIESZ-TYPE DERIVATIVESIN DOMAINS IN Rn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393A.A. Kilbas, J.J. Trujillo, A.A. VoroshilovCAUCHY-TYPE PROBLEM FOR DIFFUSION-WAVEEQUATION WITH THE RIEMANN-LIOUVILLEPARTIAL DERIVATIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403B. E. Gogovcheva, L. BoyadjievFRACTIONAL EXTENSIONS OF JACOBI POLYNOMIALSAND GAUSS HYPERGEOMETRIC FUNCTION . . . . . . . . . . . . . . . . . . 431

Anniversary: 60th ANNIVERSARY of Prof. O.I. Marichev . . . . . . . . 439

36ISSN 1311-0454 FCAA, Vol. 9, No 1 (2006)

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E.M. SaydamatovWELL-POSEDNESS OF THE CAUCHY PROBLEMFOR INHOMOGENEOUS TIME-FRACTIONALPSEUDO-DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 1V.S. Guliyev, J.J. HasanovSOBOLEV-MORREY TYPE INEQUALITY FOR RIESZPOTENTIALS, ASSOCIATED WITH THE LAPLACE-BESSELDIFFERENTIAL OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17A.A. Rousan, N.Y. Ayoub, F.Y. Alzoubi, H. Khateeb,M. Al-Qadi, M.K. Hasan(Qaseer), B.A. AlbissA FRACTIONAL LC −RC CIRCUIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33C. Abdelkefi, M. SifiON THE UNIFORM CONVERGENCE OF PARTIAL DUNKLINTEGRALS IN BESOV-DUNKL SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . 43S. Umarov, E. SaydamatovA FRACTIONAL ANALOG OF THE DUHAMEL PRINCIPLE . . . . . 57

NEW BOOK: by A. Kilbas, H.M. Srivastava and J.J. Trujillo”THEORY AND APPLICATIONS OF FRACTIONALDIFFERENTIAL EQUATIONS”,Elsevier, North-Holland Mathematics Studies, 204 . . . . . . . . . . . . . . . . . . . 71


37ISSN 1311-0454 FCAA, Vol. 9, No 2 (2006)

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Anniversary: 70th ANNIVERSARY of Prof. Megumi SAIGO . . . . . . 79

I.H. Dimovski, K.A. SkornikOPERATIONAL CALCULI FOR THE EULER OPERATOR . . . . . . . 89N. VirchenkoON THE GENERALIZED CONFLUENTHYPERGEOMETRIC FUNCTION AND ITS APPLICATION . . . . . 101A.A. Kilbas, R.K. Saxena, J.J. TrujilloKRATZEL FUNCTION AS A FUNCTIONOF HYPERGEOMETRIC TYPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109S. S. Eker, H. O. Guney, Sh. OwaON INTEGRAL MEANS FOR FRACTIONAL CALCULUSOPERATORS OF MULTIVALENT FUNCTIONS . . . . . . . . . . . . . . . . . . 133J.E. Pecaric, M. Rodic Lipanovic, H.M. SrivastavaSOME MEAN-VALUE THEOREMS OF THE CAUCHY TYPE . . . . 143V. KiryakovaON TWO SAIGO’S FRACTIONAL INTEGRAL OPERATORSIN THE CLASS OF UNIVALENT FUNCTIONS . . . . . . . . . . . . . . . . . . . 159

Report on the Book: by Anatolii A. Kilbas and Megumi Saigo,“H-TRANSFORMS. THEORY AND APPLICATIONS”,CRC Press, 2004 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177


38ISSN 1311-0454 FCAA, Vol. 9, No 3 (2006)

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Anniversary: 60th ANNIVERSARY of Prof. Khalifa TRIMECHE 181

I. Dimovski, V. Hristov, M. SifiCOMMUTANTS OF THE DUNKL OPERATORS IN C(R) . . . . . . . . 195N. Ben Salem, A. Ould Ahmed Salemy and B. SelmiMEAN-PERIODIC FUNCTIONS ASSOCIATEDWITH THE JACOBI-DUNKL OPERATOR ON IR . . . . . . . . . . . . . . . . . 215M. Assal, R. BouguilaGENERALIZED SOBOLEV SPACES OF EXPONENTIALTYPE ASSOCIATED WITH THE DUNKL OPERATORS . . . . . . . . . 237H. MejjaoliAN ANALOGUE OF BEURLING-HORMANDER’STHEOREM FOR THE DUNKL-BESSEL TRANSFORM . . . . . . . . . . . 247H. Mabroukq-HEAT OPERATOR AND q-POISSON’S OPERATOR . . . . . . . . . . . . 265A. Gasmi, M. Sifi, F. SoltaniHERZ-TYPE HARDY SPACES FOR THE DUNKLOPERATOR ON THE REAL LINE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287V.S. Guliyev, M. AssalON MAXIMAL FUNCTION ONTHE LAGUERRE HYPERGROUP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

New Book: by Peter Popivanov, “GEOMETRICAL METHODSFOR SOLVING OF FULLY NONLINEARPARTIAL DIFFERENTIAL EQUATIONS”, UBM’ 2006 . . . . . . . . . . . . 319

39ISSN 1311-0454 FCAA, Vol. 9, No 4 (2006)

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A. K. Mishra, P. GochhayatAPPLICATIONS OF THE OWA-SRIVASTAVA OPERATORTO THE CLASS OF k-UNIFORMLY CONVEX FUNCTIONS . . . . . 323M. Ilic, F. Liu, I. Turner, V. AnhNUMERICAL APPROXIMATION OF AFRACTIONAL-IN-SPACE DIFFUSION EQUATION (II)– WITH NONHOMOGENEOUS BOUNDARY CONDITIONS . . . . . . 333E. Andries, S. Umarov, S. SteinbergMONTE CARLO RANDOM WALK SIMULATIONS BASEDON DISTRIBUTED ORDER DIFFERENTIAL EQUATIONSWITH APPLICATIONS TO CELL BIOLOGY . . . . . . . . . . . . . . . . . . . . . 351M. HaddadHANKEL TRANSFORM IN QUANTUM CALCULUSAND APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

Corrigendum: Errata in the paper:“ON INTEGRAL MEANS FOR FRACTIONAL CALCULUSOPERATORS . . . ”, in FCAA 9, No 2 (2006), pp. 133-142,by S. S. Eker, H. O. Guney, Sh. Owa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

Meetings: FDA’2006: Report, Program of the Workshop . . . . . . . . . . . 387Meetings: AMADE’2006: Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398Meetings: ICHAA’2006: Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401Meetings: ASME’2007, Announcement: ”Classicand Fractional Dynamics on Continuous and DiscontinuousVector Fields”, Las Vegas, September 2007 . . . . . . . . . . . . . . . . . . . . . . . . . . 405IMI - BAS: Periodicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

40ISSN 1311-0454 FCAA, Vol. 10, No 1 (2007)

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L. Diening, S. SamkoHARDY INEQUALITY IN VARIABLE EXPONENTLEBESGUE SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1H. Mejjaoli, K. TrimecheSPECTRUM OF FUNCTIONSFOR THE DUNKL TRANSFORM ON IRd . . . . . . . . . . . . . . . . . . . . . . . . . . 19M.S. Ben Hammouda, A. NemriPOLYNOMIAL EXPANSIONS FOR SOLUTIONS OFHIGHER-ORDER BESSEL HEAT EQUATIONIN QUANTUM CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39J. Paneva-KonovskaTHEOREMS ON THE CONVERGENCE OF SERIESIN GENERALIZED LOMMEL-WRIGHT FUNCTIONS . . . . . . . . . . . . . 59L. BoyadjievSOME FRACTIONAL EXTENSIONS OFTHE TEMPERATURE FIELD PROBLEM IN OIL STRATA . . . . . . . 75

Meetings: ”FDA’2008”, Fractional Differentiation andits Applications, Ankara (Turkey), 5 - 7 November 2008Invitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99News: Version 6.0 of MATHEMATICAWolfram Research, Inc. - Press Release . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101New Book: INTEGRAL TRANSFORMS AND THEIRAPPLICATIONS (2nd Ed.), by L. Debnath and D. Bhatta . . . . . . . . . . 105New Book: THE ART OF MODELING IN SCIENCE ANDENGINEERING WITH MATHEMATICA (2nd Ed.),by D. Basmadjian and R. Farnood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

41ISSN 1311-0454 FCAA, Vol. 10, No 2 (2007)

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Yu.A. Rossikhin, M.V. ShitikovaCOMPARATIVE ANALYSIS OF VISCOELASTIC MODELSINVOLVING FRACTIONAL DERIVATIVESOF DIFFERENT ORDERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111R. BagleyON THE EQUIVALENCE OF THE RIEMANN-LIOUVILLEAND THE CAPUTO FRACTIONAL ORDER DERIVATIVESIN MODELING OF LINEAR VISCOELASTIC MATERIALS . . . . . . . 123Z. TomovskiINTEGRAL REPRESENTATIONS OF GENERALIZED MATHIEUSERIES VIA MITTAG-LEFFLER TYPE FUNCTIONS . . . . . . . . . . . . . 127T.M. Atanackovic, B. StankovicON A DIFFERENTIAL EQUATION WITHLEFT AND RIGHT FRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . 139K. DiethelmSMOOTHNESS PROPERTIES OF SOLUTIONS OF CAPUTO-TYPE FRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . 151M. Yamada, T. Matsuura, S. SaitohREPRESENTATIONS OF INVERSE FUNCTIONS BYTHE INTEGRAL TRANSFORM WITH THE SIGN KERNEL . . . . . . 161M. Zamani, M. Karimi-Ghartemani, N. SadatiFOPID CONTROLLER DESIGN FOR ROBUST PERFORMANCEUSING PARTICLE SWARM OPTIMIZATION . . . . . . . . . . . . . . . . . . . . . 169S.D. Purohit, S.L. KallaON q-LAPLACE TRANSFORMS OFTHE q-BESSEL FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Meetings: ”MIA 2008 Conference”, In honour of Prof. J. Pecaric,June 8-14, 2008, Split-Croatia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Meetings 2007 – 2008: Letter by J.A. Tenreiro Machado . . . . . . . . . . 199Meetings: ”FDA’2008”, Fractional Differentiation and its Applications,

November 5-7, 2008, Ankara-Turkey; News: Awards Announced . . 200

42ISSN 1311-0454 FCAA, Vol. 10, No 3 (2007)

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Anniversary: 40 YEARS OF CAPUTO DERIVATIVE AND80th ANNIVERSARY of Prof. Michele CAPUTO: . . . . . . . . . . . . . . . . . . 201Congratulating addresses, Foreword (by F. Mainardi)CV and Selected Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

A.D. Freed, K. DiethelmCAPUTO DERIVATIVES IN VISCOELASTICITY:A NON-LINEAR FINITE-DEFORMATION THEORYFOR TISSUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

Y. Luchko, J.J. TrujilloCAPUTO-TYPE MODIFICATIONOF THE ERDELYI-KOBER FRACTIONAL DERIVATIVE . . . . . . . . 249

F. Mainardi, R. GorenfloTIME-FRACTIONAL DERIVATIVESIN RELAXATION PROCESSES:A TUTORIAL SURVEY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

M. Caputo, F. MainardiA NEW DISSIPATION MODEL BASED ON MEMORY MECHANISM:REPRINTED PAPER from the journal“Pure and Applied Geophysics (PAGEOPH)”,vol. 91, No 1 (1971), pp. 134-147 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

International Conference: “APPCOM’08”Approximation & Computation (Nis, Serbia, Aug. 25-29, 2008)Dedicated to 60th Anniversary of Prof. Gradimir Milovanovic . . . . . . 325

Web Project: FRACALMO(FRActional CALculus MOdelling), Updated . . . . . . . . . . . . . . . . . . . . . . 326

43ISSN 1311-0454 FCAA, Vol. 10, No 4 (2007)

Contents

A. Fitouhi, N. Bettaibi, W. BinousINVERSION FORMULAS FOR THEq-RIEMANN-LIOUVILLE AND q-WEYL TRANSFORMSUSING WAVELETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

S.K. Sunanda, C. Nahak, S. NandaWITHDRAWN by the Managing Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

P.M. Rajkovic, S.D. Marinkovic, M.S. StankovicON q–ANALOGUES OF CAPUTO DERIVATIVEAND MITTAG–LEFFLER FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

J. L. Da Silva, M. Erraoui, H. OuerdianeGENERALIZED FRACTIONAL EVOLUTION EQUATION . . . . . . 375

H. Rafeiro, S. SamkoON A CLASS OF FRACTIONAL TYPE INTEGRALEQUATIONS IN VARIABLE EXPONENT SPACES . . . . . . . . . . . . . . 399

60th Years Anniversary:INSTITUTE OF MATHEMATICS AND INFORMATICS –BULGARIAN ACADEMY OF SCIENCES . . . . . . . . . . . . . . . . . . . . . . . . 422

44ISSN 1311-0454 FCAA, Vol. 11, No 1 (2008)

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Anniversary: TEN YEARS OF “FCAA” JOURNAL . . . . . . . . . . . . . . . . 1

M. Caputo, REPRINTED PAPER from the journal“Geophys. J. R. Astr. Soc.”, vol. 13, Issue 5 (1967), pp. 529-539:LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOSTFREQUENCY INDEPENDENT – II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3L.P. Castro, D. KapanadzePSEUDO-DIFFERENTIAL OPERATORS IN A WAVEDIFFRACTION PROBLEM WITH IMPEDANCE CONDITIONS . . . 15J.K. PrajapatINCLUSION PROPERTIES FOR CERTAIN CLASSES OFANALYTIC FUNCTIONS INVOLVING A FAMILY OFFRACTIONAL INTEGRAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . 27M. Benchohra, J. Henderson, S.K. Ntouyas, A. OuahabEXISTENCE RESULTS FOR FRACTIONAL FUNCTIONALDIFFERENTIAL INCLUSIONS WITH INFINITE DELAYAND APPLICATIONS TO CONTROL THEORY . . . . . . . . . . . . . . . . . . . 35Yu. LuchkoALGORITHMS FOR EVALUATION OF THE WRIGHTFUNCTION FOR THE REAL ARGUMENTS’ VALUES . . . . . . . . . . . . . 57A.D. Gadjiev, V.S. GuliyevTHE STEIN-WEISS TYPE INEQUALITY FOR FRACTIONALINTEGRALS, ASSOCIATED WITH THE LAPLACE-BESSELDIFFERENTIAL OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77N.M. Fonseca Ferreira, F.B. Duarte, M.F.M. Lima,M.G. Marcos, J.A. Tenreiro MachadoAPPLICATION OF FRACTIONAL CALCULUS IN THE DYNAMICALANALYSIS AND CONTROL OF MECHANICAL MANIPULATORS.. 91

Meetings: ”Meetings in 2008” and ”FDA’2008”, Fractional Differen-tiation and its Applications, Ankara (Turkey), 5-7 Nov. 2008 . . . 114-116Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117-118

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