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International Journal of Mathematical Analysis and Applications

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The Numerical Solution of System of Fractional Partial Differential Equations

International Journal of Mathematical Analysis and Applications
Vol.2 , No. 2, Publication Date: Apr. 25, 2015, Page: 27-34

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Authors

[1]	Khatereh Tabatabaei, Department of Mathematics, Faculty of Science, Atatürk University, Erzurum, Turkey.
[2]	Erkan Gunerhan, Department of Computer, Faculty of Engineering, Kafkas University, Kars, Turkey.

Abstract

In this paper, numericalsolution of fractional partial differential equations is obtained byfractional differential transform method. The fractional derivatives are described using Caputo sense; the method provides the solution in the form of a rapidly convergent series. From the result, it has been seen that the proposed method is very effective.

Keywords

Fractional Differential Transform Method, Fractional Partial Differential-Equations, Caputo Fractional Derivative

Reference

[01]	A. Arikoglu and I. Ozkol, Solution of fractional differential equations by using differential transform method, Chaos, Solitons and Fractals, 34:1473–1481, 2007.
[02]	J.Biazar and M.Eslami, Differential transform method for nonlinear fractional gas dynamics equation, 6(5): 1203-1206, 2011.
[03]	J.K.Zhou,Differential transformation and its applications for electrical circuits, PhD thesis, Wuhan, China: Huazhonguniversit, 1986.
[04]	I. Podlubny, Fractional Diﬀerential Equations, Academic Press, 1999.
[05]	Yu. A. Rossikhinand M. V. Shitikova, Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids, Appl. Mech. Rev., 50, 15-67, 1997.
[06]	B.Ibiş, M.Bayram and A. G. Ağargün, Applications of Fractional Differential Transform Method to Fractional Differential-Algebraic Equations, 1: 67-75, 2011.
[07]	ST.Mohyud-Din, MA.Noor, Homotopy perturbation method fornonlinear higher-order boundary value problems, Int. J. Nonlin. Sci.Numer. Sim., 9(4): 395-408, 2011.
[08]	ST. Mohyud-Din, MA. Noor, Variational iteration method forsolving higher-order nonlinear boundary value problems using He’s polynomials, Int. J. Nonlin. Sci. Numer. Sim., 9(2): 141-157,2008.
[09]	MJ. Jang, CL. Chen, YC. Liu, Two-dimensional differential transform for Partial differential equations, Appl. Math. Comput., 121:261–270, 2001.
[10]	F.Kangalgil, F.Ayaz, Solitary wave solutions for the KdVandmKdV equations by differential transform method Chaos SolitonsFractals, 41(1): 464-472, 2009.
[11]	KSV. Ravi, K. Aruna, Two-dimensional differential transformmethod for solving linear and non-linear Schrödinger equations, Chaos Solitons Fractals, 41(5): 2277-2281, 2009.
[12]	Z. Odibat, S. Momani, Numerical methods for nonlinear partial differential equations of fractional order, Appl. Math. Modelling, 32, 28-39, 2008.
[13]	S. Momani, Z. Odibat, Homotopy perturbation method for nonlinear partial differential equations of fractional order, Phys. Lett. A, 365, 345-350, 2007.
[14]	S. Momani, Z. Odibat, Comparison between homotopy perturbation method and the variational iteration method for linear fractional partial differential equations, Comput. Math. Appl., 54, 910-919, 2007.