The homotopy analysis method for fractional cauchy reaction-diffusion problems

Abstract

In this article, homotopy analysis method is successfully applied to obtain the approximate analytical solutions of the characteristic Cauchy reaction-diffusion equation with fractional time derivative. The beauty of the article is the wonderful application of Caputo fractional order time derivative. The linear interactions of the merging populations are examined using perturbation theory and the method of matched asymptotic expansions. The solutions of the problem for different particular cases are presented graphically. Copyright © 2011 The Berkeley Electronic Press. All rights reserved.