title: Numerical simulation of fractional Cable equation of spiny neuronal dendrites.
abstract: In this article, numerical study for the fractional Cable equation which is fundamental equations for modeling neuronal dynamics is introduced by using weighted average of finite difference methods. The stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. A simple and an accurate stability criterion valid for different discretization schemes of the fractional derivative and arbitrary weight factor is introduced and checked numerically. Numerical results, figures, and comparisons have been presented to confirm the theoretical results and efficiency of the proposed method.
authors: Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.
authors: N H
authors: NH
authors: Sweilam
authors: Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt.
authors: M M
authors: MM
authors: Khader
authors: Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.
authors: M
authors: M
authors: Adel
keywords: Fractional Cable equation; John von Neumann stability analysis; Weighted average finite difference approximations