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

Abstract 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. Highlights • A new two-dimensional multi-term time-fractional diffusion and diffusion. • Wave equation (2D-MT-TFD-DWE) is considered. • The analytical solution for the 2D-MT-TFD-DWE is derived. • A novel implicit difference method (IDM) for 2D-MT-TFD-DWE is proposed. • The stability and convergence of the IDM are proved by the energy method. • Numerical examples are given. [ABSTRACT FROM AUTHOR]