A New Analytic-Approximate Solution of Fokker-Planck Equation with Space-and Time-Fractional Derivatives

In this paper, the analytical solution of the space-and timefractional Fokker-Planck equation was derived by means of the homotopy analysis method (HAM). The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made, the comparisons show that the homotopy analysis method is very effective and convenient. An optimal value of the convergence control parameter is given through the square residual error. By minimizing the the square residual error, the optimal convergence-control parameters can be obtained. Several numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques and to compare with the existing results.