Numerical Solution for the Two-Dimensional Two-Sided Fractional Diffusion Equation

In this paper, a numerical solution of the two-dimensional two-sided fractional Diffusion equation has been presented. The algorithm for the numerical solution for this equation is based on finite difference method. The consistency, unconditional stability, and convergence of the fractional order numerical method are described. The numerical method has been applied to solve a practical numerical examples and comparing results with the exact solution. The results were presented in tables using the MathCAD 12 software package when it is needed. The finite difference method appeared to be effective and reliable in solving the two-dimensional twosided fractional Diffusion equation.