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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 561980, 11 pages
http://dx.doi.org/10.1155/2013/561980
Research Article

Approximate Analytic Solutions of Time-Fractional Hirota-Satsuma Coupled KdV Equation and Coupled MKdV Equation

School of Mathematical Sciences, Inner Mongolia University, 235 West Daxue Road, Hohhot 010021, China

Received 29 October 2012; Accepted 28 January 2013

Academic Editor: Abdel-Maksoud A. Soliman

Copyright © 2013 Jincun Liu and Hong Li. 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

By introducing the fractional derivative in the sense of Caputo and combining the pretreatment technique to deal with long nonlinear items, the generalized two-dimensional differential transform method is proposed for solving the time-fractional Hirota-Satsuma coupled KdV equation and coupled MKdV equation. The presented method is a numerical method based on the generalized Taylor series expansion which constructs an analytical solution in the form of a polynomial. The numerical results show that the generalized two-dimensional differential transform method is very effective for the fractional coupled equations.