A Numerical Method for the Solution of the Two-Dimensional Time-Fractional Cable Equation of Distributed-Order Involving Riesz Space-Fractional Operators

Abstract

this paper, we propose an efficient hybrid numerical approach to obtain approximate solutions to the two-dimensional time-fractional cable equation of distributed-order involving Riesz space-fractional operators. This combined numerical approach includes two numerical approaches in time and space directions. The weighted and shifted Gr & uuml;nwald difference numerical method is used to approximate the fractional problem in the time direction, and the fractional compact numerical method is applied in the direction of the space variable. The stability and convergence analyses are studied for the proposed numerical approach. To show the effectiveness of the presented numerical method, some numerical examples are given, and the numerical results for these examples are plotted. Also, this numerical approach is compared with other methods.