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Abstract and Applied Analysis
Volume 2014, Article ID 601961, 16 pages
http://dx.doi.org/10.1155/2014/601961
Research Article

Applications of the Novel ( )-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) Equation

Department of Mathematics, Faculty of Sciences, HITEC University, Taxila 47080, Pakistan

Received 17 February 2014; Revised 24 April 2014; Accepted 12 May 2014; Published 18 June 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 Muhammad Shakeel 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

We use the fractional derivatives in modified Riemann-Liouville derivative sense to construct exact solutions of time fractional simplified modified Camassa-Holm (MCH) equation. A generalized fractional complex transform is properly used to convert this equation to ordinary differential equation and, as a result, many exact analytical solutions are obtained with more free parameters. When these free parameters are taken as particular values, the traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. Moreover, the numerical presentations of some of the solutions have been demonstrated with the aid of commercial software Maple. The recital of the method is trustworthy and useful and gives more new general exact solutions.