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

Abstract

In this paper, the analytical solution of the space-and timefractionalFokker-Planck equation was derived by means of the homotopyanalysis method (HAM). The fractional derivatives are describedin the Caputo sense. Some examples are given and comparisons aremade, the comparisons show that the homotopy analysis method is veryeffective and convenient. An optimal value of the convergence controlparameter is given through the square residual error. By minimizing thethe square residual error, the optimal convergence-control parameterscan be obtained. Several numerical examples are considered aiming todemonstrate the validity and applicability of the proposed techniquesand to compare with the existing results.