An approximate analytical solution of nonlinear fractional diffusion equation by homotopy analysis method

Abstract

In the present paper, the approximate analytical solution of a nonlinear diffusion equation with fractional time derivative () and with the diffusion term as () are obtained with the help of analytical method of nonlinear problem called the Homotopy Analysis Method (HAM). By using initial value, the explicit solution of the equation for different particular cases have been derived which demonstrate the effectiveness, validity, potentiality and reliability of the method in reality. Numerical results of the fast and slow diffusion for different particular cases are presented graphically. The numerical solutions show that only a few iterations are needed to obtain accurate approximate solutions. Key words: Partial differential equation, nonlinear fractional diffusion equation, Brownian motion, homotopy analysis method.