  In this paper, we discuss the time-space Caputo-Riesz fractional diffusion
equation with variable coefficients on a finite domain. The finite difference
schemes for this equation are provided. We theoretically prove and numerically
verify that the implicit finite difference scheme is unconditionally stable
(the explicit scheme is conditionally stable with the stability condition
$\frac{\tau^{\gamma}}{(\Delta x)^{\alpha}}+\frac{\tau^{\gamma}}{(\Delta
y)^{\beta}} <C$) and 2nd order convergent in space direction, and
$(2-\gamma)$-th order convergent in time direction, where $\gamma \in(0,1]$.
