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Mathematical Problems in Engineering
Volume 2015, Article ID 364853, 9 pages
http://dx.doi.org/10.1155/2015/364853
Research Article

Differential Transform Method with Complex Transforms to Some Nonlinear Fractional Problems in Mathematical Physics

1Faculty of Sciences, HITEC University, Taxila Cantonment 44000, Pakistan
2Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
3Department of Mathematics, College of Science, Ain Shams University, Abbassia, Cairo 11566, Egypt

Received 28 May 2015; Revised 31 August 2015; Accepted 28 September 2015

Academic Editor: Fazal M. Mahomed

Copyright © 2015 Syed Tauseef Mohyud-Din 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.

Abstract

This paper witnesses the coupling of an analytical series expansion method which is called reduced differential transform with fractional complex transform. The proposed technique is applied on three mathematical models, namely, fractional Kaup-Kupershmidt equation, generalized fractional Drinfeld-Sokolov equations, and system of coupled fractional Sine-Gordon equations subject to the appropriate initial conditions which arise frequently in mathematical physics. The derivatives are defined in Jumarie’s sense. The accuracy, efficiency, and convergence of the proposed technique are demonstrated through the numerical examples. It is observed that the presented coupling is an alternative approach to overcome the demerit of complex calculation of fractional differential equations. The proposed technique is independent of complexities arising in the calculation of Lagrange multipliers, Adomian’s polynomials, linearization, discretization, perturbation, and unrealistic assumptions and hence gives the solution in the form of convergent power series with elegantly computed components. All the examples show that the proposed combination is a powerful mathematical tool to solve other nonlinear equations also.