Abstract
In this paper, an efficient numerical scheme is constructed for a generalized fractional sub-diffusion problem using a newly proposed generalized weighted shifted Grünwald-Letnikov (gWSGL) approximation for the generalized fractional derivative. The solvability, stability and convergence of the numerical scheme are analyzed using the discrete energy method. It is proven that the temporal convergence order is 2 and this is the best result to date. Simulation is further carried out to demonstrate the accuracy of the proposed numerical scheme.
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