A Difference Method For A Class Of Time Distributed-order And Space Riesz Fractional Diffusion Equation

In this article,we consider a class of time distributed-order and space Riesz frac-tional order diffusion equation with the initial boundary value satisfying the Dirchlet boundary condition. Firstly, the integral term in the distributed-order is discretized with a mid-point quadrature rule, the equation is transformed into the multi-term Caputo fractional order diffusion equation and space Riesz fractional order diffusion equa-tion. Then, we discretized the the multi-term Caputo fractional order derivatives in the equation using the L2 - 1? interpolation format, for the space Riesz fractional derivative,we use linear interpolation and fractional order center difference quotient to approximated,thus we constructed the numerical method and proved the stability and convergence of the method and got the order of convergence of numerical methods is O(?2 + h2 + (??)2) ,among them.??h??? indicates the time step, the space step,the order step length.Finally, Numerical experiments show that the theoretical analysis of numerical methods is consistent with the results, and also indicates the validity of numerical methods.