Numerical computations for the solution of time-fractional diffusion equation with a distributed-order Riemann-Liouville derivative

In this paper, a nonlinear distributed order Riemann Liouville time fractional diffusion equation is analyzed. We use finite difference schemes to approximate the integer order derivatives and a series approximation for the time fractional derivative to achieve an implicit numerical method. The stability and convergence of the proposed implicit method are considered where show a linear order convergence in time and a second order convergence in space. These theoretical results are in agreement with the computations of the numerical approximations. In the computation experiments, different linear and nonlinear examples are examined where the computed errors show the efficiency of the scheme.

Keywords:

Distributed order fractional diffusion equation , approximate , computationsRiemann-Liouville derivative , finite difference scheme , stability analysis.