Abstract: In this paper, an efficient numerical method is proposed to solve the CaputoRiesz fractional diffusion equation with fractional Robin boundary conditions. We
approximate the Riesz space fractional derivatives using the fractional central difference
scheme with second-order accurate. A priori estimation of the solution of the numerical
scheme is given, and the stability and convergence of the numerical scheme are analyzed.
Finally, a numerical example is used to verify the accuracy and efficiency of the numerical
method.

Key words:  Fractional boundary conditions, Stability and convergence, Caputo-Riesz
fractional diffusion equation