A numerical scheme for solving Space-Fractional equation by finite differences theta-method

This paper aims to present a general framework of the θ − and spatial extrapolation method. We examine θ −method to solve Fractional Diffusion Differential Equations and we use spatial extrapolation for improving results (0 ≤ θ ≤ 1). We use Riemann-Liouville derivative based on Shifted Grunwald stimates for fractional derivative. Consistency, stability and convergence analysis of the method is discussed. At the end, two illustrative 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 θ − method • Riemann-Liouville derivative • Shifted Grunwald formula