Abstract

In this paper, the homotopy perturbation method (HPM) is employed to obtain approximate analytical solutions of the time-fractional reaction-diffusion equation of the Fisher type. The method can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. The analytical/numerical results are compared with existing analytic solutions obtained by Adomian decomposition method (ADM) and differential transformation method (DTM) and the outcomes confirm that the scheme yields accurate and excellent results even when few components are used.

Key words: Fisher equation, diffusion, reaction, fractional partial differential equations.