In this paper, we consider the Fokker-Planck equation (FPE) and the Fokker- Planck equation with space- and time-fractional derivatives. The Fokker-Planck equation arises in various fields in chemistry, natural science, including astrophysics problems, biological applications, chemical physics and other fields. Transforming the Fokker-Planck equation into optimization problem and using polynomial basis functions, we obtain the system of algebraic equation. Then, we solve the system of nonlinear algebraic equation and we have the coefficients of polynomial basis functions expansion. We extensively discuss the convergence of the method. Illus- trative examples are included to demonstrate the validity and applicability of the technique.
