Stability Of Finite Difference Method For Delay Time Fractional Diffusion Equation

In this paper,we consider the numerical solution of the initial boundary value problem of the delay time fraction diffusion equation(?)where 0<a<1,L>0,T>0,p(x,t),K(x,t),k0(t)and k1(t)are continuous functions.(?)au(x,t)/(?)t?is Caputo fractional derivative with ? order.We transformed the fractional derivative of Caputo into Riemann-Liouville fractional integral,then we use Lubich's linear multistep method to discrete Riemann-Liouville fractional integral and second-order central difference is used for the space derivative.We obtain the numerical method for solving that problems and prove the stability of method.The feasibility of the method is verified by numerical experiments.