A numerical approach to the generalized nonlinear fractional Fokker–Planck equation

In this paper, we propose a fully discrete Galerkin finite element method to solve the generalized nonlinear fractional Fokker–Planck equation, which has a multi-fractional-spatial-operator characteristic that describes the Lévy flight. In the time direction, we use the finite difference method, and in the spatial direction we use the fractional finite element method in the framework of the fractional Sobolev spaces. We derive a fully discrete scheme for the considered equation. We prove the existence and uniqueness of the discrete solution and give the error estimates. The numerical examples are also included which support the theoretical analysis.