Meshless local Petrov-Galerkin method for 2D fractional Fokker-Planck equation involved with the ABC fractional derivative

This paper examines a time fractional version of the 2D Fokker-Planck equation involved with the Atangana-Baleanu-Caputo fractional derivative, under the Dirichlet boundary conditions. A fully discretization approach based on the meshless local Petrov-Galerkin method and (3 - fl) -order approximation is proposed for this equation. More precisely, we apply the meshless local Petrov-Galerkin method based on the Moving Kriging interpolation to discretize the space domain, and utilize the (3 - fl) -order approximation together with the theta- weighted finite difference method to discretize the temporal domain. By implementing this method, we get a solution for the problem by solving a system of algebraic equations. The validity of the method is investigated by solving four examples.