Semi-analytical solution for time-fractional diffusion equation based on finite difference method of lines (MOL)

In this article, we apply the method of lines (MOL) for solving the time-fractional diffusion equations (TFDEs). The use of MOL yields a system of fractional differential equations with the initial value. The solution of this system could be obtained in the form of Mittag–Leffler matrix function. A direct method which computes the Mittag–Leffler matrix by applying its eigenvalues and eigenvectors analytically has been discussed. The direct approach has been applied on one-, two-, and three-dimensional TFDEs with Dirichlet, Neumann, and periodic boundary conditions as well.