A SPACE-TIME SPECTRAL COLLOCATION METHOD FOR SOLVING THE VARIABLE-ORDER FRACTIONAL FOKKER-PLANCK EQUATION

A numerical approach for solving the variable-order fractional Fokker-Planck equation (VO-FFPE) is proposed. The computational scheme is based on the shifted Legendre Gauss-Lobatto and the shifted Chebyshev Gauss-Radau collocation methods. The VO-FFPE is written as a truncated series of shifted Legendre and shifted Chebyshev polynomials for space and time variables, respectively. The residuals of the VO-FFPE at the shifted Legendre Gauss-Lobatto and shifted Chebyshev Gauss-Radau quadrature points are estimated. The original problem is converted into a system of algebraic equations that can be solved easily. Several examples are presented to demonstrate the efficacy of the technique.