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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 482419, 12 pages
http://dx.doi.org/10.1155/2013/482419
Research Article

Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations

1Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia
2Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
3Mathematics Department, Faculty of Science, El-Minia University, El-Minia, Egypt

Received 27 June 2013; Accepted 24 September 2013

Academic Editor: Mehmet Sezer

Copyright © 2013 Khaled A. Gepreel 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 implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. The fractional derivatives are described in the Caputo sense. These methods are used in applied mathematics to obtain the analytic approximate solutions for the nonlinear Bejamin-Bona Mahoney (BBM) partial fractional differential equation. We compare between the approximate solutions obtained by these methods. Also, we present the figures to compare between the approximate solutions. Also, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved -expansion function method to find exact solutions of nonlinear fractional BBM equation.