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Journal of Applied Mathematics
Volume 2014, Article ID 192519, 12 pages
http://dx.doi.org/10.1155/2014/192519
Research Article

Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method

1Faculty of Science, Suez Canal University Ismailia, Ismailia, Egypt
2The High Institute of Administration and Computer, Port Said University, Port Said, Egypt

Received 25 May 2013; Revised 3 January 2014; Accepted 4 January 2014; Published 3 March 2014

Academic Editor: Magdy A. Ezzat

Copyright © 2014 M. A. Mohamed and M. Sh. Torky. 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

The Legendre multiwavelet Galerkin method is adopted to give the approximate solution for the nonlinear fractional partial differential equations (NFPDEs). The Legendre multiwavelet properties are presented. The main characteristic of this approach is using these properties together with the Galerkin method to reduce the NFPDEs to the solution of nonlinear system of algebraic equations. We presented the numerical results and a comparison with the exact solution in the cases when we have an exact solution to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.