A NUMERICAL METHOD FOR THE SPACE-TIME FRACTIONAL CONVECTION-DIFFUSION EQUATION
空间-时间分数阶对流扩散方程的数值解法

In this paper, a space-time fractional convection-diffusion equation is considered. The equation is obtained from the classical convection-diffusion equation by replacing the first-order time derivative, the second-order space derivative with fractional derivatives of order $\alpha$($0<\alpha<1$), $\beta$ ($1<\beta<2$)respectively. An implicit difference scheme is presented. It is shown that the method is unconditional stable and the convergence order of the method is $O(\tau+h)$ . Finally, some numerical examples are given.