On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations

Abstract

In this paper, we consider numerical solutions for Riesz space fractional partial differential equations with a second order time derivative. We propose a Galerkin finite element scheme for both the temporal and spatial discretizations. For the proposed numerical scheme, we derive sharp stability estimates as well as optimal a priori error estimates. Extensive numerical experiments are conducted to verify the promising features of the newly proposed method.

On Unconditionally Stable New Modified Fractional Group Iterative Scheme for the Solution of 2D Time-Fractional Telegraph Model

“…Many techniques have been used to solve fractional partial differential equations using the Caputo and the Caputo-Fabrizio type operators [14][15][16]. Lai and Liu [17] solved the second order fractional partial differential equation using the Galerkin finite element method and Riesz fractional derivative. Akram et al [18,19] proposed unconditionally stable methods for the fractional hyperbolic models via B-spline approaches.…”