Editorial Fractional Differential Equations...

Hindawi Publishing CorporationInternational Journal of Differential EquationsVolume 2013, Article ID 802324, 2 pageshttp://dx.doi.org/10.1155/2013/802324

EditorialFractional Differential Equations 2012

Fawang Liu,1 Om P. Agrawal,2 Shaher Momani,3 Nikolai N. Leonenko,4 and Wen Chen5

1 School of Mathematical Sciences, Queensland University of Technology, P.O. Box 2434, Brisbane, QLD 4001, Australia2 Department of Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, IL 62901, USA3Department of Mathematics, The University of Jordan, Amman 11942, Jordan4 School of Mathematics, Cardiff University, Cardiff CF2 4YH, UK5Department of Engineering Mechanics, Hohai University, Xikang Road No. 1, Nanjing, Jiangsu 210098, China

Correspondence should be addressed to Fawang Liu; f.liu@qut.edu.au

Received 8 January 2013; Accepted 8 January 2013

Copyright © 2013 Fawang Liu et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

It is our pleasure to bring this third special issue of theInternational Journal of Differential Equations dedicated toFractional Differential Equations (FDEs).

In recent years, a growing number of papers by manyauthors from various fields of science and engineering dealwith dynamical systems described by fractional partial differ-ential equations. Due to the extensive applications of FDEsin engineering and science, research in this area has grownsignificantly all around the world.

This third special issue on fractional differential equationsconsists of one review article and 9 original articles coveringvarious aspects of FDEs and their applications written byprominent researchers in the field.

In the paper titled as “Generalized multiparameters frac-tional variational calculus” by O. P. Agrawal, the authorintroduces some new one-parameter GFDs, investigates theirproperties, and uses them to develop several parts of FVC.The author also shows that many of the fractional derivativesand fractional variational formulations proposed recentlyin the literature can be obtained from the GFDs and thegeneralized FVC.

The papers titled as “Solving the fractional Rosenau-Hyman equation via variational iteration method and homo-topy perturbation method,” by R. Y. Molliq and M. S. M.Noorani, titled as “Generalized monotone iterative techniquefor Caputo fractional differential equation with periodicboundary condition via initial value problem” by J. D. Ramı́rezandA. S. Vatsala, and titled as “Solving fractional-order logisticequation using a new iterative method” by S. Bhalekar and

V. Daftardar-Gejji introduce variational iteration and homo-topy perturbation methods for solving fractional Rosenau-Hyman, fractional differential (with periodic boundary con-ditions), and fractional-order logistic equations, respectively.

The paper titled as “Axisymmetric solutions to time-fractional heat conduction equation in a half-space underRobin boundary conditions,” by Y. Z. Povstenko derivesanalytical solutions to time-fractional heat equation in a half-space under Robin boundary conditions using an integraltransform technique. The paper titled as “Analytical study ofnonlinear fractional-order integrodifferential equation: revisitVolterra’s population model” by N. A. Khan et al. proposes atwo-component homotopy method to solve Volterra’s popu-lation model.

The paper titled as “A time-space collocation spectralapproximation for a class of time fractional differential equa-tions” by F. Huang develops a time-space collocation spectralmethod for a class of time fractional differential equations.

The paper titled as “Analysis of Caputo impulsive fractionalorder differential equations with applications” by L. Mahtoet al. studies the existence and uniqueness of the theoremof Caputo impulsive fractional order differential equationsusing Sadavoskii’s fixed point method. The paper titled as“Fractional order difference equations” by J. J.Mohan andG. V.S. R. Deekshitulu establishes a theorem on the existence anduniqueness of solutions for various classes of fractional orderdifference equations.

Finally, The paper titled as “Chaos control and synchro-nization in fractional-order Lorenz-like system” by S. Bhalekar

2 International Journal of Differential Equations

investigates Chaos control and synchronization in fractional-order Lorenz-like system.

Thus, this special issue provides a wide spectrum ofcurrent research in the area of FDEs, andwe hope that expertsin this and related fields find it useful.

Fawang LiuOm P. AgrawalShaher Momani

Nikolai N. LeonenkoWen Chen

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