A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. Accurate numerical solutions are achieved in the Chebyshev collocation method subject to both Dirichlet and Neumann boundary conditions. The solution obtained by these hybrid methods allows for the evaluation at any point in time without the need for time-marching to a particular point in time.
B. A. Jacobs. C. Harley. "Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations." Abstr. Appl. Anal. 2014 (SI40) 1 - 10, 2014. https://doi.org/10.1155/2014/757204