SDC/FDM scheme for Caputo-Hadamard type fractional diffusion equation

This paper develops an efficient algorithm for the time-space fractional diffusion equation with Caputo-Hadamard derivative in time and fractional Laplacian in two space dimensions. For the time discretization, the spectral deferred correction (SDC) method is utilized. In the mean while, the fractional centered finite difference formula is adopted to approximate the two-dimensional fractional Laplacian. Numerical example is presented to illustrate the effectiveness of the propose scheme.