Numerical Treatments For The Space- Time Fractional FokkerPlanck Equation By Means of Homotopy Perturbation Natural Transform Method

Abstract

In the present paper, an efficient approach based on homotopy perturbation method by using natural transform is adopted to solve some linear and non-linear space-time fractional Fokker-Planck Equations (FPE) in closed form. The space and time fractional derivatives are considered in Caputo sense. The homotopy perturbation natural transform method is a combined form of natural transform, homotopy perturbation method and He's polynomials. 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 result shows the effectiveness and good accuracy of the method. Keywords: Fokker-Planck Equation, Caputo fractional derivative, Natural transform, Homotopy perturbation method.