Numerical computation of fractional multi-dimensional diffusion equations by using a modified homotopy perturbation method

The main aim of the present work is to present a numerical algorithm for solving fractional multi-dimensional diffusion equations which describes density dynamics in a material undergoing diffusion by using a modified homotopy perturbation method with the help of the sumudu transform. The modified homotopy perturbation method is not limited to the small parameter, such as in the classical perturbation method. The method gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.