Numerical solution of Fokker–Planck equation with space- and time-fractional derivatives

This Letter presents numerical solutions for the space- and time-fractional Fokker–Planck equation using the variational iteration method and the Adomian decomposition method. The fractional derivatives are described in the Caputo sense. The methods give an analytic solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. Some examples are given and comparisons are made, the comparisons show that the variational iteration method is very effective and convenient and overcome the difficulty arising in calculating Adomian polynomials. The numerical results show that the two approaches are easy to implement and accurate when applied to space- and time-fractional Fokker–Planck equations. The methods introduce a promising tool for solving many space–time fractional partial differential equations.