Compact finite difference method to numerically solving a stochastic fractional advection-diffusion equation

In this paper, a stochastic space fractional advection diffusion equation of Itô type with one-dimensional white noise process is presented. The fractional derivative is defined in the sense of Caputo. A stochastic compact finite difference method is used to study the proposed model numerically. Stability analysis and consistency for the stochastic compact finite difference scheme are proved. Two test examples are given to test the performance of the proposed method. Numerical simulations show that the results obtained are compatible with the exact solutions and with the solutions derived in the literature.