Solution of Nonlinear Fractional Diffusion Equation Using Similarity Transform and Homotopy Analysis Method

Abstract

In this article, the Similarity transformation is used to reduce the fractional order nonlinear diffusion equation to a fractional order differential equation, which is solved approximately using Homotopy analysis method. A special effort has been given to show the effect of reaction term with long term correlation to the diffusion equation for various values of anomalous exponent. Effects of parameters on the solution profile through speeding up the convergence of approximate solution by the analysis of minimization of error are calculated numerically and presented through graphs for different particular cases.