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Journal of Applied Mathematics
Volume 2015, Article ID 357861, 9 pages
http://dx.doi.org/10.1155/2015/357861
Research Article

Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method

1Department of Mathematics, Faculty of Science, Taif University, Taif 888, Saudi Arabia
2Department of Mathematics, Faculty of Science, Al Azhar University, Cairo 11884, Egypt
3Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt

Received 9 September 2014; Accepted 26 December 2014

Academic Editor: Md Sazzad Hossien Chowdhury

Copyright © 2015 Mohamed S. Mohamed 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

User friendly algorithm based on the optimal homotopy analysis transform method (OHATM) is proposed to find the approximate solutions to generalized Abel’s integral equations. The classical theory of elasticity of material is modeled by the system of Abel integral equations. It is observed that the approximate solutions converge rapidly to the exact solutions. Illustrative numerical examples are given to demonstrate the efficiency and simplicity of the proposed method. Finally, several numerical examples are given to illustrate the accuracy and stability of this method. Comparison of the approximate solution with the exact solutions shows that the proposed method is very efficient and computationally attractive. We can use this method for solving more complicated integral equations in mathematical physical.