Solution of the time- and Riesz space-fractional Fokker-Planck equation by a stable Gaussian radial basis function method

In this article the Caputo time- and Riesz space-fractional Fokker-Planck equation (TSFFPE) is solved by the stable Gaussian radial basis function (RBF) method. By a spatial discretization and using the Riesz fractional derivative of the stable Gaussian radial basis function interpolants computed in [23], the computations of TSFFPE reduced to a system of fractional ODEs. A high order finite difference method is presented for this system of ODEs, and the computations are converted to a system of linear or nonlinear algebraic equations, in each time step. In the nonlinear case, these systems can be easily solved by the Newton iterative method. Numerical illustrations are performed to confirm the accuracy and efficiency of the presented method. Some comparisons are made with the results in other literature.

Solution of the time- and Riesz space-fractional Fokker-Planck equation by a stable Gaussian radial basis function method Keywords:

Caputo derivative , Fractional Fokker-Planck equation , Radial basis functions , Riesz derivative