Finite difference scheme for time‐space fractional diffusion equation with fractional boundary conditions.

In this paper, the finite difference scheme is developed for the time‐space fractional diffusion equation with Dirichlet and fractional boundary conditions. The time and space fractional derivatives are considered in the senses of Caputo and Riemann‐Liouville, respectively. The stability and convergence of the proposed numerical scheme are strictly proved, and the convergence order is O(τ2−α+h2). Numerical experiments are performed to confirm the accuracy and efficiency of our scheme. [ABSTRACT FROM AUTHOR]