Finite Element Method for the Space and Time Fractional Fokker–Planck Equation

Abstract

We develop the finite element method for the numerical resolution of the space and time fractional Fokker-Planck equation, which is an effective tool for describing a process with both traps and flights; the time fractional derivative of the equation is used to characterize the traps, and the flights are depicted by the space fractional derivative. The stability and error estimates are rigorously established, and we prove that the convergent order is O(k(2-alpha) + h(mu)), where k is the time step size and h the space step size. Numerical computations are presented which demonstrate the effectiveness of the method and confirm the theoretical claims.