Applied Mathematics & Information Sciences

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In this paper, a non-standard Crank-Nicholson finite difference method (NSCN) is presented. NSCN is used to study numerically the variable-order fractional Cable equation, where the variable order fractional derivatives are described in the Riemann- Liouville and the Gr¨unwald-Letnikov sense. The stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. The reliability and efficiency of the proposed approach are demonstrated by some numerical experiments. It is found that NSCN is preferable than the standard Crank-Nicholson finite difference method (SCN).