A Fractional Finite Difference Method for Solving the Fractional Poisson Equation Based on the Shifted Grünwald Estimate

Abstract

In this study a fractional Poisson equation is scrutinized through finite difference using the shifted Grünwald estimate. A novel method is proposed numerically. The existence and uniqueness of the solution for the fractional Poisson equation is proved. Exact and numerical solutions are constructed and compared. Then numerical results show the efficiency of the proposed method.

Keywords

• Fractional Poisson equation
• Riemann-Liouville fractional derivative
• Shifted Grünwald Estimate
• Taylor’s expansion of fractional order