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International Journal of Differential Equations
Volume 2011 (2011), Article ID 237045, 12 pages
http://dx.doi.org/10.1155/2011/237045
Research Article

Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives

Department of Mathematics, Neyshabour Branch, Islamic Azad University, Neyshabour, Iran

Received 4 May 2011; Accepted 12 May 2011

Academic Editor: Shaher M. Momani

Copyright © 2011 Hadi Hosseini Fadravi 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

The analytical solution of the foam drainage equation with time- and space-fractional derivatives was derived by means of the homotopy analysis method (HAM). The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made; the comparisons show that the homotopy analysis method is very effective and convenient. By choosing different values of the parameters 𝛼 , 𝛽 in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained.