The analytical solution and numerical solutions for a two-dimensional multi-term time fractional diffusion and diffusion-wave equation

In this paper we consider the analytical and numerical solutions for a two-dimensional multi-term time-fractional diffusion and diffusion-wave equation. We derive the analytical solution for the equation using the method of separation of variables and properties of the multivariate Mittag-Leffler function. An implicit difference approximation is constructed. Stability and convergence analysis of the numerical scheme are proved by the energy method. Numerical examples are constructed to evaluate the working of the numerical scheme as compared to theoretical analysis.