Numerical solution for Poisson fractional equation via finite differences theta-method

In this paper we examine -method for solving fractional Possion differential equations for(0 ≤ θ ≤ 1). Consistency, stability and convergence analysis of the method is discussed. At the end, numerical examples have been presented. The obtained results reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems.

Fractional PDE (FPDE), Finite differences theta-method, Riemann-Liouville derivative, Shifted Grunwald formula.