A novel finite difference scheme for time fractional diffusion-wave equation with singular kernel

Abstract

In this paper, we suggest a novel numerical approximation of the CaputoFabrizio fractional derivative of order α (1 < α < 2). Our novel discretization is found by using discret fractional derivative at t = tk with new coefficients e−(α−1)(tk−tm+ 1/2)/2−α − e−(α−1)(tk−tm− 1/2) 2−α . Also, we prove that the difference scheme is unconditionally stable.