Abstract: In this paper, three implicit finite difference methods are developed to solve one dimensional time fractional advection-diffusion equation. The fractional derivative is treated by applying right shifted Gr¨unwald-Letnikov formula of order α∈(0, 1). We investigate the stability analysis by using von Neumann method with mathematical induction and prove that these three proposed methods are unconditionally stable. Numerical results are presented to demonstrate the effectiveness of the schemes mentioned in this paper.

Key words: Time fractional advection-di?usion, Finite di?erence method, Gr?unwald-Letnikov formula, Stability, E?ectiveness