Abstract
In this paper, we consider a modified time distributed-order anomalous sub-diffusion equation for the description of processes becoming less anomalous over the course of time. First, we discretize the integral term using a mid-point quadrature rule and transform the time distributed-order fractional diffusion equation into a multi-term equation. Then applying the backward difference method in time and Galerkin finite element method in space, we present a fully discrete scheme to solve the time distributed-order fractional diffusion equation. Moreover, the stability and convergence of the proposed method are also discussed. Numerical examples are given to verify the accuracy and stability of our scheme.
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