The finite element method for the generalized space fractional Fokker-Planck equation

Abstract

In this paper, we derive the finite element method for the numerical solution of the Generalized space fractional order (fractional for simplicity) Fokker-Planck equation, which the space fractional derivatives are the left and right Riemann-Liouville derivatives that can be used to describe Lévy flights. The fully discrete numerical approximation is analyzed, where the Galerkin finite element method for the space Riemann-Liouville fractional derivatives with order 1 + β ∈ [1, 2) and γ ∈ (0, 1]. Results on variational solution of the error estimates are presented. Numerical examples are included to confirm the theoretical estimates.