An explicit finite difference approximation for space-time Riesz-Caputo variable order fractional wave equation using Hermitian interpolation

Variable order fractional operators can be used in various physical and biological applications where rates of change of the quantity of interest may depend on space and/or time. In this paper, we propose an explicit finite difference approximation for a space-time Riesz-Caputo variable order fractional wave equation with initial and boundary conditions in a finite domain. The proposed scheme is conditionally stable and has global truncation error $O(\tau^2+h^2)$. We also present a numerical experiment to verify the efficiency of the proposed scheme.