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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 803902, 8 pages
http://dx.doi.org/10.1155/2014/803902
Research Article

Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations

1Faculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), 71800 Nilai, Malaysia
2Department of Mathematics, Zawia University, Zawia, Libya
3Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 7 September 2013; Revised 12 November 2013; Accepted 3 December 2013; Published 22 January 2014

Academic Editor: Hossein Jafari

Copyright © 2014 Asma Ali Elbeleze 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 apply the homotopy perturbation method to obtain the solution of partial differential equations of fractional order. This method is powerful tool to find exact and approximate solution of many linear and nonlinear partial differential equations of fractional order. Convergence of the method is proved and the convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. The fractional derivatives are described in the Caputo sense. Some examples are presented to verify convergence hypothesis and simplicity of the method.