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 ? (1 < ? < 2). Our novel discretization is found by using discret fractional derivative at t = tk with new coefficients e?(??1)(tk?tm+ 1/2)/2?? ? e?(??1)(tk?tm? 1/2) 2?? . Also, we prove that the difference scheme is unconditionally stable.