NATIONAL CONFERENCE ON MATHEMATICAL ANALYSIS AND …€¦ · Acknowledgement The Organizers of the National Conference on Mathematical Analysis and Applications are thankful to Prof

NATIONAL CONFERENCE ON

MATHEMATICAL ANALYSIS

AND APPLICATIONS

December 19-20, 2019

Supported by

Department of Mathematics

NATIONAL INSTITUTE OF TECHNOLOGYTIRUCHIRAPPALLI – 620 015

NATIONAL CONFERENCE ON

MATHEMATICAL ANALYSIS

AND APPLICATIONS

December 19-20, 2019


NATIONAL INSTITUTE OF TECHNOLOGYTIRUCHIRAPPALLI – 620 015

Acknowledgement

The Organizers of the National Conference on MathematicalAnalysis and Applications are thankful to Prof. Mini ShajiThomas, Director, Shri. A. Palanivel, Registrar, and Prof.M. Umapathy, Dean Research and Consultancy, NIT-T fortheir support and co-operation. We also thank the membersof the advisory committee for their help. The invited speak-ers and the participants have a special place in the successof this conference. Prof. M. Lakshmanan, Prof. K. Balachan-dran, Prof. Tanmay Basak, and other speakers have readilyagreed to deliver the talks at our conference. Some of theinvited speakers have traveled a long distance; in particular,Dr. Lee See Keong came from Malaysia, Dr. Anbhu Swami-nathan came from Roorkee, Prof. Vellaisamy from Mumbai,Dr. Naveen Jain, Dr. Kanika Khatter, and Dr. Lakhveer Kaurcame from Delhi, Dr. S. B. Joshi from Maharastra and Dr.S. Sivasubramanian from Tindivanam. We are thankful to allthese invited speakers for coming and sharing their researchwork. We are also thankful to the young scholars who havecome here to present their research work and to other partic-ipants for their interest. Our faculty, research scholars, andnon-teaching staff have their share in organizing this confer-ence.

The conference is supported by Science and Engineering Re-search Board (SERB), Department of Science and Technology,GoI and Tamil Nadu State Council for Science and Technol-ogy, Department of Higher Education, Government of TamilNadu. We acknowledge their financial support with thanks.

Contents

About the Department 1

About the Conference 4

Programme 5

Invited Talks 6

M. Lakshmanan, Dynamics of a Class of NonlinearNonstandard Type Lagrangian / HamiltonianOscillators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Tanmay Basak, Finite Element Analysis of MultipleSteady Flow and Thermal Fields with BifurcationsDuring Natural Convection within Cavities . . . . . . . . . . . 6

S. Sivasubramanian , On Univalent Functions that areStarlike with Respect to a Boundary Point . . . . . . . . . . . 7

Anbhu Swaminathan, Extension of Stable Functionsand Vietoris Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

K. Balachandran, Controllability and Stability ofFractional Dynamical Systems . . . . . . . . . . . . . . . . . . . . . . . 9

P. Vellaisamy, Analysis of intersections of trajectoriesof systems of linear fractional differential equations . . . 10

See Keong Lee, The Class U(λ, µ) and Some of itsProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Naveen Kumar Jain, Bohr Radius for Janowski StarlikeFunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Kanika Khatter, Radius Problems for certain classes ofAnalytic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

S.B. Joshi, Subclasses of Harmonic Univalent Functions 12

Lakhveer Kaur, Bilinearization and Analytic Solutionsof Some Partial Differential Equations . . . . . . . . . . . . . . . . 12

Contributed Talks 13

Sindhu Murugan, Odd Factor Decomposition of H-VSuper Magic Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

T. Sajitha Kumari, Analytic Even Mean Labeling ofSnake Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

S. Kavitha, Radial Movement Optimization Algorithmfor Cubic Objective Function With Equality andInequality Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Debananda Basua, Existence and Uniqueness ofSolutions for a Fractional Boundary Value Problem . . . 15

S. Sangeetha, Unsteady Natural Convective Flow ofa Nanofluid Past an Infinite Vertical Plate in thePresence of Radiation and Chemical Reaction . . . . . . . . 16

S. Kavitha, Toeplitz Determinants for BazilevicFunctions Connected with Sine Functions . . . . . . . . . . . . . 17

Adiba Naz, Generalized Bessel function associatedwith the exponential function . . . . . . . . . . . . . . . . . . . . . . . . . 17

Vibha Madaan, Janowski Starlike and Convex Radiiof Some Entire Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

A. Murugan, Certain Geometric Properties ofGeneralized Struve Functions . . . . . . . . . . . . . . . . . . . . . . . . . 18

K. Dhurai, On the Subclasses of Univalent FunctionsStarlike with Respect to a Boundary Point . . . . . . . . . . . 19

Shalu Yadav, Bohr’s Radius for Classes of α-spiralFunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Asha Sebastian, Radius Problems for Functions in theClass S∗(α,δ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

R. Kanaga, Radius of Starlikeness for Certain AnalyticFunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

S. Madhumitha, Radius of Parabolic Starlikeness ofSpriallike Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Sudhir Singh, Travelling Wave Solutions of Time-Fractional Benjamin-Ono Equation . . . . . . . . . . . . . . . . . . . 21

K. Aarthika, Two Parameter Singularly PerturbedReaction-Convection-Diffusion Problem . . . . . . . . . . . . . . 22

S. Saravanakumar, Partial Stability of BooleanNetworks with Impulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

C. Mattuvarkuzhali, Optimal Controls and StabilityBehavior of Infinite Order Stochastic FractionalDifferential Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

J. Priyadharsini, Existence of Solution of FuzzyFunctional Stochastic Differential Equations withImpulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Praveen Kumar Rajan, A SEIR Model for HumanPapillomavirus Transmission. . . . . . . . . . . . . . . . . . . . . . . . . . 24

Other Participants 25

Speaker Index 26

1


National Institute of TechnologyTiruchirappalli

About the Department

The Institute. The National Institute of Technology (for-merly known as Regional Engineering College) Tiruchirap-palli, situated in the heart of Tamil Nadu on the banks ofriver Cauvery, was started as a joint and co-operative ventureof the Government of India and the Government of TamilNadu in 1964 with a view to catering to the needs of man-power in technology for the country. The college has been con-ferred with autonomy in financial and administrative mattersto achieve rapid development. Because of this rich experi-ence, this institution was granted Deemed University Statuswith the approval of the UGC/AICTE and Govt. of Indiain the year 2003 and renamed as National Institute of Tech-nology. NITT is an Institution of National Importance underthe Ministry of Human Resource and Development (MHRD),Government of India. NIT-T was registered under SocietiesRegistration Act XXVII of 1975.

The Institute has been imparting technical education in corebranches of science and engineering, besides pushing the fron-tier areas in research. With a vibrant campus and enviable fa-cilities, the Institute provides 10 undergraduate, 29 postgrad-uate and Ph.D. programmes. NITT is ranked no. 1 among theNITs, and 10th in the National Institutional Ranking Frame-work (NIRF), MHRD, Govt. of India.

The hallmark of the campus is the good facilities which catersto the academic and extracurricular interests of the students.The Octagon is the pride of the campus equipped with modern

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facilities like a CAD/CAM Lab, Local Area Network, High-Speed Internet connection, and other seminar and conferencefacilities. It is maintained and run by the Computer SupportGroup (CSG) of the institute.

Apart from this, the campus provides ample opportunitiesfor developing extracurricular skills which include NCC, NSS,Students Chapters of IEEE, social clubs, and sports & games.The Alumni of this institution have excelled in various spheresand are positioned very well globally in a number of leadingGovernment, Public Sector & Private Organizations.

NIT-T hosts two intercollegiate fests namely Festember (Cul-tural) and Pragyan (Technical) and an inter-department festnamely NITTfest (Cultural) annually. These fests draw stu-dents from most colleges of South India and are hugely popu-lar. Apart from this, each department conducts Symposium.

The institute has a total campus area of 800 acres. Thisincludes good hostel facilities, Hospital, Post & Telegraph,Telecom Center, fully computerized State Bank of India (SBI)NIT branch with ATM facility, Bookstall, Reprographic Cen-ter, Canteen, Swimming pool and Co-op. Stores.

NITT is located in Thuvakudi on the Trichy-Tanjore nationalhighway, about 20 km from the Trichy Airport/Railway Junc-tion/Bus Stand.

The Department. The Department of Mathematics is oneof the pioneering and the most distinguished departmentsin NITT. Applying multi-disciplinary research and teachingmethods, the department strongly believes in finding math-ematical solutions for various social-economic, technologicaland work related processes and challenges. The department iscommitted to outstanding graduate training to produce lead-ing scholars in various fields of mathematics. Since its incep-tion, the department has been supporting Ph.D. graduates to

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carry out challenging research work of wide ranging industrialand social implications. From the academic year 2019-20, thedepartment is offering M.Sc. Mathematics.

The following are the faculty members of the department:

Professors HAG• Prof. R. Ponalagusamy• Prof. K. Murugesan• Prof. T.N. Janakiraman

Professors• Prof. D. Deivamoney Selvam• Prof. V. Kumaran• Prof. V. Ravichandran• Prof. P. Saikrishnan

Associate Professors• Dr. R. Tamil Selvi• Dr. V. Lakshmana Gomathi Nayagam• Dr. V. Shanthi

Assistant Professors• Dr. I. Jeyaraman• Dr. N. Prakash• Dr. Jitraj Saha• Dr. Vamsinadh Thota

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About the Conference

The main objective of the conference is to provide platform foracademicians, researchers, students and industry professionalsto present their research work and to be a stage for exchang-ing ideas in the field of mathematics and applied mathemat-ics. This national conference cover the topics like Differentialequations, Real and Complex Analysis, Functional Analysis,Numerical Analysis, Optimization.

Organizing Committee

• Prof. K. Murugesan, Chairman

• Prof. V. Ravichandran, Convenor

• Prof. P. Saikrishnan, Secretary

• Dr. R. Tamil Selvi, Secretary

• All other faculty members of the department

Advisory Committee

• Prof. Dhirendra Bahuguna, IIT Kanpur

• Prof. K. Balachandran, Bharathiar University

• Prof. P. Balasubramaniam, GRI, Gandhigram

• Prof. B. K. Dass, University of Delhi

• Prof. Varsha Gejji, Savitribai Phule Pune University

• Prof. M. Lakshmanan, Bharathidasan University

• Prof. A. K. Nandhakumaran, IISc Bangalore

• Prof. S. Ponnusamy, IIT Madras

• Prof. R. Sakthivel, Bharathiar University

• Prof. N. Selvaraju, IIT Guwahati

• Prof. R. Shagadevan, Madras University

• Prof. Anbhu Swaminathan, IIT Roorkee

• Prof. P. Vellaisamy, IIT Bombay

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Programme

ProgramDay – I (19.12.2019)

09.00am - 09.30am Registration09.30am - 10.00am Inauguration10.00am – 10.15am Tea Break10.15am – 11.00am Invited Talk I111.00am – 11.45am Invited Talk I211.45am – 01.00pm Session – I (T12-T16)01.00pm – 02.00pm Lunch Break02.00pm – 02.30pm Invited Talk I302.30pm – 03.00pm Invited Talk I403.30pm – 03.45pm Tea Break03.45pm – 05.00pm Session – II (T17-T22)

Day – II (20.12.2019)

09.30am - 10.15am Invited Talk I510.15am – 11.00am Invited Talk I611.00am – 11.30am Tea Break11.30am – 12.00pm Invited Talk I712.00pm – 12.30pm Invited Talk I812.30pm – 01.00pm Invited Talk I901.00pm – 02.00pm Lunch Break02.00pm – 02.30pm Invited Talk I1002.30pm – 03.00pm Invited Talk I1103.00pm - 03.45pm Session - III (T23-T25)03.45pm – 04.00pm Tea Break04.00pm – 05.30pm Session - IV (T26-T31)

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Invited Talks

Dynamics of a Class of Nonlinear Nonstandard I1Type Lagrangian / Hamiltonian Oscillators

M. LakshmananDepartment of Nonlinear Dynamics, School of Physics, Bharathi-

dasan University, Tiruchirappalli – 620024

e-mail: [email protected], [email protected]

Considering a generalized class of Lienard type nonlinear sec-ond order differential equations and their coupled versions, weidentify that a subclass of these systems possesses a nonstan-dard Lagrangian / Hamitonian description. We also studythe associated nonlinear dynamics and solutions based onsymmetry analysis and linearizing transformations. The sys-tems identified include Mathews–Lakshmanan oscillator anda PT–symmetric generalized Emden type equation and theirhigher dimensional variants. We also report their quantumproperties. Infinite hierarchies of the above class of equationsin the form of generalized Riccati and Abel equations andtheir coupled versions are also reported.

Finite Element Analysis of Multiple Steady Flow I2and Thermal Fields with Bifurcations During Nat-ural Convection within Cavities

Tanmay BasakDepartment of Chemical Engineering, IIT Madras, Chennai-600036

e-mail: [email protected]

A Brinkman extended Darcy model has been used to studythe effect of spatial nonuniformity of wall temperatures on themultiplicity of steady convective flows within a square porous

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enclosure saturated with low Prandtl fluid (Pr = 0.026). Theconvection is assumed to be driven by the hotter bottom wallin conjunction with colder side walls, where bottom-side walljunctions maintain continuity of temperature to represent amore realistic situation. This configuration enforces nonuni-formity on either bottom wall or side walls or both bottomand side wall temperatures. The degree of nonuniformity ofwall temperatures are varied parametrically in terms of ther-mal aspect ratio (Θ) to simulate various possible scenarios ofnonuniform bottom/side wall temperatures and steady solu-tion branches are traced in the parameter space of Θ to in-vestigation of variation of multiplicity of the flows. A pertur-bation technique has been used to initiate the steady solutionbranches, which are then traced by numerical continuationscheme. A penalty finite element approximation in conjunc-tion with Newton-Raphson method and parameter continua-tion scheme has been used to construct the bifurcation dia-grams of various steady branches. This work reveals 3 steadysymmetric branches and 4 steady asymmetric branches withexhibition of symmetry breaking bifurcation. This work alsoshows that the nonuniformity of wall temperatures play a cru-cial role for the existence of multiple solutions as well as themultiplicity of convective flows.

On Univalent Functions that are Starlike withI3Respect to a Boundary Point

S. SivasubramanianDepartment of Mathematics, University College of Engineering

Tindivanam, Anna University Tindivanam 604001


The classical field of analytic univalent functions is a fascinat-ing area of study and research with continued interest evenin recent times. The interest in this field which is classified

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under the broader area of Geometric Function Theory is ba-sically due to interplay of geometry and analysis. In view ofthe Riemann mapping theorem, any simply connected domainwhich is not the entire complex plane is conformally equiva-lent to the open unit disk U = {z : |z| < 1}, and hence theentire study of the Geometric function theory is only on theunit disk. The name univalent functions or Schlicht functionsis given to functions defined on the open unit disc U of thecomplex plane that are characterized by the fact that such afunction takes in U, a value not more than once and mapsU onto a Schlicht domain(a German word indicating a regionwhich is not self overlapping and which contains no branchpoints). Let A denote the class of all functions f of the formf(z) = z+a2z

2 + · · · , which are analytic in the open unit diskU, and let S be a subclass of A consisting of univalent func-tions. Let f(z) and g(z) be analytic in U. Then the functionf(z) is subordinate to g(z), if there exists a Schwarz functionw(z), analytic in U with w(0) = 0 and |w(z)| < 1 (z ∈ U),such that f(z) = g(w(z))(z ∈ U). We denote this subordina-tion by f ≺ g or f(z) ≺ g(z) (z ∈ U). A function f is saidto be starlike, if f maps the unit disk U univalently onto a do-main D that is starlike with respect to the origin. This meansthat for all t, 0 < t < 1, and all z, z ∈ U, tf(z) ∈ D. In otherwords tf(z) is subordinate to f(z) in D. A function f ∈ A issaid to be starlike of order α, 0 ≤ α < 1, written as f ∈ S∗(α),if Re (zf ′(z)/f(z)) > α, z ∈ U. For α = 0, the functions in theclass S∗(α) are starlike with respect to the origin ( in generalstarlike). A function f is said to be convex of order α in U,if and only if zf ′ ∈ S∗(α) and f(0) = 0. In this case for allα, 0 ≤ α < 1, f(U) is a convex domain. In particular, a convexfunction is starlike of order 1/2. Even though the class of allstarlike functions of order α, S∗(α) was explored extensivelyby many authors for 0 ≤ α < 1, M. S. Robertson [Univalentfunctions starlike with respect to a boundary point, J. Math.Anal. Appl. 81 (1981), no. 2, 327–345] felt that not muchseemed to be known about the class of analytic functions G(z)

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that map U onto domains D that are starlike with respect toa boundary point. Considering this as a gap in the field ofinterest, he defined the class of Univalent functions starlikewith respect to a boundary point. This boundary point wastaken to be G(1) where G(1) = limr→1G(r), 0 < r < 1, isassumed to exist and where G(0) = 1. In this situation thedomain D has the property that tG(z) + (1 − t)G(1) ∈ D,0 < t ≤ 1, z ∈ U. Few examples were given for the class offunctions that are starlike with respect to a boundary point.The aim of this lecture it to outline this concept with relevantworks. Few scope for further works will be discussed.

Extension of Stable Functions and Vietoris Theo-I4rem

Anbhu SwaminathanDepartment of Mathematics, IIT Roorkee, Roorkee-247667


Ruscheweyh obtained the concept of stable function for thepartial sum of certain analytic functions by means of sub-ordination. This concept of stable functions is extended byseveral researchers recently. We provide an outline of theserecent developments and further applications. This concept ofstable function uses an extended form of the known theoremof Vietoris for the positivity of certain trigonometric sums.

Controllability and Stability of Fractional Dy-I5namical Systems

K. BalachandranDepartment of Mathematics, Bharathiar University, Coimbatore

e-mail: balachandran [email protected]

TBA

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Analysis of intersections of trajectories of sys- I6tems of linear fractional differential equations

P. VellaisamyDepartment of Mathematics, IIT Bombay, Powai, Mumbai-400076


In this talk, we discuss the trajectorial intersections in sys-tems of linear fractional differential equations. We propose aclassification of intersections of trajectories into three classes:(a) trajectories intersecting at the same time (IST), (b) tra-jectories intersecting at different times (IDT) and (c) self-intersections of a trajectory. We prove a generalization ofseparation theorem for the case of linear fractional systems.This result proves the existence of the IST. Based on the pres-ence of the IST, systems are further classified into two typesnamely Type I and Type II systems, which are analyzed fur-ther for the IDT. Self-intersections in a fractional trajectorycan be regular such as constant solution or limit-cycle behav-ior or they can be irregular such as cusp or node. We givenecessary and sufficient condition for a trajectory to be regu-lar.

The Class U(λ, µ) and Some of its Properties I7

See Keong LeeSchool of Mathematical Sciences, Universiti Sains Malaysia, 11800

USM, Penang, MALAYSIA


Let D = {z : |z| < 1} be the unit disc on the complex planeC. The class U(λ, µ) , which consists of analytic functionsf(z) = z +

∑∞n=2 anz

n satisfying |(z/f(z))2f ′(z)− µ| < λ forall z ∈ D, 0 < λ ≤ 1 and µ ∈ C, will be studied. Among theproperties to be investigated are the sizes of the parameters µ

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and λ that ensure the univalence of f , coefficient bounds andsome radii problem.

Bohr Radius for Janowski Starlike FunctionsI8

Naveen Kumar JainDepartment of Mathematics, Aryabhatta College, Delhi-110021


For an analytic f(z) =∑∞

n=0 anzn mapping the unit disc D

into D, it is well-known that∑∞

n=0 |anzn| ≤ 1 for |z| ≤ 1/3and the number 1/3, known as the Bohr radius for the class ofanalytic functions mapping D into D, is sharp. In this paper,the Bohr radius is determined for the class of Janowski star-like functions which yields Bohr radius for many subclasses ofanalytic functions.

Radius Problems for certain classes of AnalyticI9Functions

Kanika KhatterDept. of Mathematics, Hindu Girls College, Sonepat, Haryana


Let P be the class of functions defined on open unit disk hav-ing positive real part. In this talk, we discuss three classes ofnormalized analytic functions f satisfying one of the follow-ing conditions: (i) f(z)/g(z) ∈ P and ((1 − z2)/z)g(z) ∈ Pfor some analytic function g, (ii)

∣∣∣f(z)/g(z) − 1∣∣ < 1 and

((1 − z2)/z)g(z) ∈ P for some analytic function g and (iii)((1 − z2)/z)f(z) ∈ P . Various radii have been estimated forthe functions in the above defined classes to belong to vari-ous previously known classes of analytic functions such as theclasses of starlike functions of order α, and parabolic starlike

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functions, as well as to the subclasses of starlike functions as-sociated with lemniscate, reverse lemniscate, lune, cardioid orto exponential function, sine function and a rational function.

Subclasses of Harmonic Univalent Functions I10

S.B. JoshiDepartment of Mathematics, Walchand College of Engineering,

Sangli, Maharashtra

e-mail: santosh. [email protected]

We present an introduction of harmonic mappings with somebasic results along with known facts of analytic functions.Further we will present connections and analogous part of har-monic with analytic functions. Lastly, results on subclassesof harmonic univalent functions will be discussed.

Bilinearization and Analytic Solutions of Some Par- I11tial Differential Equations

Lakhveer KaurDepartment of Mathematics, Jaypee Institute of Information Tech-

nology, Noida (U.P.)


In current course of study, we emphasize on obtaining newanalytic solutions for some nonlinear partial differential equa-tions (NLPDEs) by considering their bilinear forms. The for-mulation of bilinear equations of NLPDEs are obtainted withthe help of Hirota’s method and Bell polynomials. Futher-more, novel test function has been appointed to formally de-rive various exact solutions containing abundant arbitraryconstants. New solutions consist of hyperbolic, trigonomet-ric and exponential functions. 3-dimensional plots of all ex-act solutions, determined in this research, may provide rich

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mathematical aspects of concerned physical phenomenon. Also,innovative as well as distinct exact solutions raised, by thismanner, may hold powerful applications in various fields ofmathematical physics.

Contributed Talks

Odd Factor Decomposition of H-V Super Magic GraphsT12

Sindhu MuruganScott Christian College(Autonomous), Nagercoil-629003

e-mail: msindhu [email protected]

An H-magic labeling in an H-decomposable graph G is a bi-jection f : V (G)∪E(G)→ {1, 2, . . . , p+q} such that for everycopy H in the decomposition

∑v∈V (H) f(v) +

∑e∈E(H) f(e) is

constant. The function f is said be H-V super magic labelingif f(V (G)) = {1, 2, . . . , p}. We show that certain even regularand odd regular graphs have an (2k + 1)-factor H-V supermagic decomposition, for k ≥ 1.

Analytic Even Mean Labeling of Snake GraphsT13

T. Sajitha KumariScott Christian College(Autonomous), Nagercoil- 629001


Let G(V,E) be a graph with p vertices and q edges. A (p, q)-graph is called an analytic even mean graph if there exist aninjective function f from the vertex set to {0, 2, 4, 6, ..., 2q}such that when each edge e = uv with f(u) < f(v) is labeledwith f ∗(uv) = d|(f(u) + 1))2 − (f(v))2|/2e if f(u) 6= 0 andf ∗(uv) = d(f(v))2/2e if f(u) = 0 and all the edge labels areeven. We prove triangular snake, alternate triangular snake,double triangular snake, double alternate triangular snake,

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quadrilateral snake, alternate quadrilateral snake admit ana-lytic even mean labeling.

Joint work with M. Regees (Malankara Catholic College, Maria-giri) and S. Chandra Kumar (Scott Christian College (Au-tonomous), Nagercoil)

Radial Movement Optimization Algorithm for Cu- T14bic Objective Function With Equality and Inequal-ity Constraints

S. KavithaDepartment of Mathematics, Kunthavai Naacchiyaar Governemnt

Arts College for Women, Thanjavur – 613007

e-mail: kavitha [email protected]

The optimization problem with cubic objective function withequality and inequality constraints is a non-linear problem.The practical optimization problems of economic power dis-patch are realistically modeled as the cubic equation. Theobjective of economic power dispatch problem is to find opti-mal power generation of committed generating units in ther-mal power station that minimize the total fuel cost subjectto satisfying equality constraint, that is total generation isequal to total power demand, and inequality constraints, thatis power generation of units must lie within operating lim-its. Most conventional methods used quadratic equations toexpress their characteristic curves. The existing conventionalmethods fail to impose generation limits in economic powergeneration scheduling problem and find difficulty in dealingwith cubic cost function which reflects nonlinearity of the ac-tual generator response to quadratic optimization problem.Due to the complexity of solving optimization with cubicoptimization problem, the problem is approximated. Thisrough approximation of the optimization problem formula-tion makes the solution deviated from the optimality. The

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optimization problem with cubic objective function, an equal-ity constraint and a set of inequality constraints are definedby min f(x) =

∑ni=1 aix

3i + bix

2i + cixi + di subject to the

equality constraint∑n

i=1 xi = xT and inequality constraintsxli ≤ xi ≤ xui , xi ≥ 0 where ai, bi, ci and di are the coefficientsof the variable xi, XT is the sum of the decision variables, land u are the lower and upper bounds of the variable xi. Inthis paper, radial movement optimization algorithm is imple-mented to find the optimal solution for the problem with cu-bic objective function. Radial movement optimization (RMO)algorithm is developed by Rasoul Rahmani et al. for nonlin-ear optimization problems. It is a swarm based optimizationalgorithm. The computational steps RMO algorithm are ini-tailialisation, generating the initial velocity vector, locatingthe centre point, finding the radial movement of the particle,evaluating the fitness of the particles, searching around globalbest (Gbest) particle, finding new centre location and the fit-ness of radial best vector (Rbest) is compared with the fitnessof Gbest vector. If Rbest is better than Gbest, Gbest is re-placed by Rbest and the iteration is incremented by one. Theadvantages of the RMO are the number of control parametersis less; it requires lesser computer memory, fast convergenceand provides global optimal solution for the practical opti-mization problem. The suitability of the proposed approachis demonstrated with sample test system consisting of threegenerating units. The simulation result shows that the pro-posed method provides optimal solution that minimizes theobjective function and satisfies the practical constraints.

Existence and Uniqueness of Solutions for a Frac-T15tional Boundary Value Problem

Debananda BasuaDepartment of Mathematics, Birla Institute of Technology and Sci-

ence - Pilani, Hyderabad Campus, Hyderabad - 500078


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In this paper, we are concerned with the fractional bound-ary value problem{

(Dαa y)(t) + f(t, y(t)) = 0, a < t < b,

y(a) = 0, (Dβay)(b) = 0,

where 1 < α ≤ 2, Dαa is the αth-order Riemann–Liouville

fractional derivative, 0 ≤ β ≤ 1 and f : [a, b] × R → R is acontinuous function. We obtain a few existence and unique-ness results for the above problem by using some fixed pointtheorems.

Joint work with J. M. Jonnalagadda ([email protected])

Unsteady Natural Convective Flow of a Nanofluid T16Past an Infinite Vertical Plate in the Presence ofRadiation and Chemical Reaction

S. SangeethaDepartment of Mathematics, Anna University, Chennai-600025


Effect of radiation and chemical reaction of an unsteady freeconvective flow of a nanofluid over an infinite vertical platecarried out using Laplace transform technique. Graphical il-lustration of various parameters on velocity, Temperature andconcentration as well as Skin friction, Nusselt number are pre-sented. It is noticed that the velocity increase with increasingvalue of thermal Grashof number and mass Grashof numberand also increasing value of thermal radiation decreases thetemperature of the fluid.

Joint work with P. Loganathan ([email protected])

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Toeplitz Determinants for Bazilevic Functions Con-T17nected with Sine Functions

S. KavithaDepartment of Mathematics, SDNB Vaishnav College for Women,

Chromepet, Chennai 600064


Motivated by the earlier works on Toeplitz Determinants byV. Radhika, S. Sivasubramanian, G. Murugusundaramoorthy,Jay M. Jahangiri [Toeplitz matrices whose elements are thecoefficients of functions with bounded boundary rotation, J.Complex Anal. 2016, Art. ID 4960704, 4 pp. & Toeplitz ma-trices whose elements are coefficients of Bazilevic functions,Open Math. 16 (2018), no. 1, 1161–1169], we consider theToeplitz matrices whose elements are coefficients of Bazilevicfunctions and obtain upper bounds for Toeplitz determinantsfor initial values that are connected with sine functions.

Joint work with Thomas Rosy (Madras Christian College) andG. Murugusundaramoorthy, (Vellore Institute of Technology,Vellore)

Generalized Bessel function associated with theT18exponential function

Adiba NazDepartment of Mathematics, University of Delhi, Delhi–110 007


Sufficient conditions are obtained on the parameters of thegeneralized Bessel function under which this special functionbecome exponential convex and exponential starlike in theopen unit disk. The method of differential subordination isemployed in proving the results.

Joint work with Sumit Nagpal and V. Ravichandran

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Janowski Starlike and Convex Radii of Some En- T19tire Functions

Vibha MadaanDepartment of Mathematics, University of Delhi, Delhi–110 007


The radii of starlikeness and convexity associated with Janowskifunction (1+Az)/(1+Bz), where−1 ≤ B < A ≤ 1, have beendetermined for the normalizations of the Jackson and Hahn-Exton q-Bessel functions and that of the Lommel function offirst kind. The Jackson and Hahn-Exton q-Bessel functionsare q-generalizations of the Bessel function of first kind. TheHadamard factor representation and the interlacing propertyof zeros of these functions with the zeros of their derivativesare used as the key tools to obtain the radii for respectivenormalizations.

Joint work with Ajay Kumar (University of Delhi) and V.Ravichandran (NIT-T).

Certain Geometric Properties of Generalized Stru- T20ve Functions

A. MuruganDepartment of Mathematics, University College of Engineering

Tindivanam, Anna University, Tindivanam-604001

e-mail: muru [email protected]

The objective of the present work is to establish certain geo-metric properties including close-to-convexity (univalency),starlikeness and convexity in the unit disc by using the thegeneralized struve functions with their normalization. Resultsobtained for certain classes are new and for the other classesfor which similar results exist in the literature. The authorshope this article will motivate the future researchers to work

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in the area of struve function which can find many applica-tions in field of differential equations and Special functions.

Joint work with V. Radhika (Easwari Engineering College,Chennai) and S. Sivasubramanian (Anna University Tindi-vanam)

On the Subclasses of Univalent Functions StarlikeT21with Respect to a Boundary Point

K. DhuraiDepartment of Mathematics, Government College of Engineering,

Dharmapuri 636704


We have introduced a new subclass of univalent starlike func-tions with respect to a boundary point as done by H. Silver-man. A systematic investigation of the new subclass is done.In particular, we have obtained the Herglotz representaion ofthese starlike function and certain related estimates.

Joint work with S. Sivasubramanian (Anna University Tindi-vanam)

Bohr’s Radius for Classes of α-spiral FunctionsT22

Shalu YadavDepartment of Mathematics NIT Tiruchirappalli


A class of analytic functions f(z) =∑∞

n=0 anzn in the unit

disc D satisfies a Bohr phenomenon if there exists an r∗ > 0such that

∞∑n=1

|anzn| ≤ d(f(0), ∂f(D))

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for every function f in the given class and for every z with|z| = r ≤ r∗. The largest r∗ is the Bohr radius for the class.We discuss the Bohr’s inequality for the starlike function oforder α, convex functions of order α and α-spiral functions.The obtained results are shown to be sharp.

This is a joint work with Naveen Kumar Jain.

Radius Problems for Functions in the Class S∗(α,δ) T23

Asha SebastianDepartment of Mathematics, NIT, Tiruchirappalli-620015 India


We discuss several radius problems using subordination of thenormalized analytic functions f defined on the open unit disksatisfying the inequality Re ((zf ′(z)/f(z))(1 + αzf ′′(z)/f(z)))> δ. In particular, the radii of Janowski starlikeness, star-likeness of order β of these functions are determined. Otherclasses examined are the classes of starlike functions associ-ated with lemniscate of Bernoulli and the exponential func-tion.

This is a joint work with V. Ravichandran.

Radius of Starlikeness for Certain Analytic Func- T24tions

R. KanagaDepartment of Mathematics, NIT, Tiruchirappalli-620015


The radius of starlikeness of normalized analytic functions fdefined on the unit disk that satisfies Re 2f(z)/(2z + z2) > 0is computed.

This is a joint work with V. Ravichandran

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Radius of Parabolic Starlikeness of Spriallike Func-T25tions

S. MadhumithaDepartment of Mathematics, NIT, Tiruchirappalli-620015


Radius problems are usually solved by finding estimates forthe real part of associated expression whenever the classesare defined by using the class of functions with positive realpart. When the associated region is not a half-plane, we needto compute the region of values to find radius. In this talk,we compute radius of the largest disk centered at an arbitrarypoint (a, b) to be completely contained in the parabolic region|w− 1| < Rew and use it to determine the radius of parabolicstarlikeness of spirallike functions.

Travelling Wave Solutions of Time-Fractional Ben-T26jamin-Ono Equation

Sudhir SinghDepartment of Mathematics, NIT, Tiruchirappalli-620015


The exact solutions for the nonlinear time-fractional Benjamin-Ono equation via the exp (−Φ(ε))−expansion scheme is ob-tained. Specifically, the model studied in the sense of con-formable fractional derivative. The achieved travelling wavesolutions are structured in rational, trigonometric (periodicsolutions) and hyperbolic functions (solitary wave solutions).The exact derived solutions could be very significant in elabo-rating physical aspects of real-world phenomena. We have 2Dand 3D illustrations for free choices of the physical parameterto understand the physical explanation of the problems.

This is a joint work with K. Murugesan

22

Two Parameter Singularly Perturbed Reaction- T27Convection-Diffusion Problem

K. AarthikaDepartment of Mathematics, NIT, Tiruchirappalli-620015


In this paper, presented the two-parameter system of singu-larly perturbed reaction-convection-diffusion of the discontin-uous problem. An effective finite-difference scheme wieldedon the non-uniform mesh. In the theory part, we confirmthat our scheme converges almost first-order uniformly withrespect to the parameters. Numerical examples are providedto verify the analytical results.

This is a joint work with Dr. V. Shanthi.

Partial Stability of Boolean Networks with Im- T28pulses

S. SaravanakumarDepartment of Mathematics, The Gandhigram Rural Institute

(Deemed to be University), Gandhigram - 624 302


The partial stability result for the Boolean networks withimpulses has been derived. First, the Boolean networks ischanged into impulsive linear discrete-time system under theframework of semi-tensor product of matrices. Through thesolutions of discrete-time dynamical system and their obtainedpartial stability results a new signal encryption algorithm isproposed and the encryption signal is achieved. For the appli-cation aspects, it is shown that the resulting encrypted signalis entirely different from the original signal.

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Joint work with P Muthukumar (Gobi Arts and Science Col-lege, Gobichettipalayam) and P. Balasubramaniam (The Gand-higram Rural Institute - Deemed to be University)

Optimal Controls and Stability Behavior of In-T29finite Order Stochastic Fractional DifferentialEquation

C. MattuvarkuzhaliDepartment of Mathematics, Gandhigram Rural Institute - Deemed

to be University, Gandhigram - 624 302


We are concerned the fractional stochastic differential equa-tion (FSDEs) with non-local effect driven by sub-fractionalBrownian motion(sub-fBm) and Poisson jump in this study.The existence and uniqueness solution for FSDEs is verifiedthrough Picard’s iteration. Further we investigate the con-trollability and stability to the consider system. Lastly theobtained result is verified through numerical simulation.

Joint work with P. Balasubramaniam (The Gandhigram RuralInstitute - Deemed to be University)

Existence of Solution of Fuzzy Functional Sto-T30chastic Differential Equations with Impulse

J. PriyadharsiniDepartment of Mathematics, The Gandhigram Rural Institute -

Deemed to be University, Gandhigram - 624 302


Stochastic differential equations represent equipment in mod-eling of a dynamic systems operating with fuzzy settings drivenby stochastic noise. In this manuscript, a new kind of equa-tion namely fuzzy functional stochastic differential equation

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(FFSDE) is proposed. It is defined by stochastic integral ofa fuzzy process with respect to m-dimensional Brownian mo-tion. In this paper, the results of existence and uniquenessof impulsive FFSDE are obtained with generalised Hukuharaderivative by using contraction principle.

Joint work with P. Balasubramaniam (The Gandhigram RuralInstitute - Deemed to be University)

A SEIR Model for Human Papillomavirus Trans- T31mission

Praveen Kumar RajanDepartment of Mathematics, NIT, Tiruchirappalli-620015


A Suspectable-Exposed-Infected-Recovered model for HumanPapillomavirus infection transmission to women which pro-gresses to cervical cancer is investigated. The disease-freeequilibrium state of the model is determined. Using the next-generation matrix method, the cancer reproduction numberis computed in terms of the model parameters and used as athreshold value. We show that, if the reproduction numberis less than unity, the disease-free equilibrium is stable oth-erwise unstable and the existence and uniqueness of endemicequilibrium also proved. Finally, numerical simulations arecarried out to obtain an analytic results.

This is a joint work with K. Murugesan.

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Other Participants

The following are participating without presenting any paper:

• C. Amulya Smyrna, VIT University, Chennai• K. Chandrasekran, Jeppiaar SRR Engineering College• T. Divyadevi, NIT-T• P. Gayathri, NIT-T• A. Sahaya Jenifer, NIT-T• Meghna, University of Delhi• K. Sakthivel, RMK Engineering College, Kavaraipettai• Somya, NIT-T• P. Swarnambigai, Vellore Institute of Technology, Chennai• Sangeetha K V, NIT-T

Speaker Index

Aarthika, K., 22

Balachandran, K., 9Basak, Tanmay, 6Basua, Debananda, 15

Dhurai, K., 19

Jain, Naveen Kumar, 11Joshi, S.B., 12

Kanaga, R., 20Kaur, Lakhveer, 12Kavitha, S., 14, 17Khatter, Kanika, 11

Lakshmanan, M., 6Lee, See Keong, 10

Madaan, Vibha , 18Madhumitha, S., 21

Mattuvarkuzhali, C., 23Murugan, A., 18Murugan, Sindhu, 13

Naz, Adiba, 17

Priyadharsini, J., 23

Rajan, Praveen Kumar, 24

Sajitha Kumari, T., 13Sangeetha, S., 16Saravanakumar, S. , 22Sebastian, Asha, 20Singh, Sudhir, 21Sivasubramanian , S., 7Swaminathan, Anbhu, 9

Vellaisamy, P., 10

Yadav, Shalu, 19

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Notes 27

28 Notes

Notes 29

In pic: Rockfort temple, Kallanai dam and Tanjore big temple

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NATIONAL CONFERENCE ON MATHEMATICAL ANALYSIS AND …€¦ · Acknowledgement The Organizers of the National Conference on Mathematical Analysis and Applications are thankful to Prof