Finite difference scheme for a fractional telegraph equation with generalized fractional derivative terms

Abstract

In this paper, a finite difference scheme is presented for the Generalized Time-Fractional Telegraph Equation (GTFTE) defined using Generalized Fractional Derivative (GFD) terms introduced recently. The generalization of fractional derivatives is done by introducing scale and weight functions, and for their particular choices, GFD reduces to Caputo and Riemann–Liouville derivatives. We present the solution behaviour of the GTFTE by changing the weight and scale functions in GFD. The convergence and the stability of the finite difference scheme (FDS) are also presented, and for the numerical simulation of the FDS, we consider examples which validate our numerical method. © 2019 Elsevier B.V.