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Abstract and Applied Analysis
Volume 2013, Article ID 717540, 9 pages
http://dx.doi.org/10.1155/2013/717540
Research Article

Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method

Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt

Received 23 September 2013; Accepted 7 November 2013

Academic Editor: Tie-cheng Xia

Copyright © 2013 A. A. Hemeda. 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

An extension of the so-called new iterative method (NIM) has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM) and the variational iteration method (VIM) reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.