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A finite difference approximation for the Caputo fractional derivative of the  4-β, 1 < β ≤ 2 order has been developed. A difference schemes for solving the  Dirihlet’s problem of the Poisson’s equation with fractional derivatives has  been applied and solved. Both the stability of difference problem in its  right-side part and the convergence have been proved. A numerical example was  developed by applying both the Liebman and the Monte-Carlo methods

The Dirihlet problem for the fractional Poisson’s equation with Caputo derivatives: A finite difference approximation and a numerical solution