Numerical approximations of Atangana–Baleanu Caputo derivative and its application

Abstract

To solve the problems of non-local dynamical systems, Caputo and Fabrizio proposed a new definition for the fractional derivative. Atangana and Baleanu generalized the Caputo-Fabrizio derivative using the Mittag–Leffler function as the kernel which is both non-singular and non-local. In this paper, we investigate numerical schemes for the Atangana–Baleanu Caputo derivative in two ways and use the same for solving Advection-Diffusion equation whose time derivative is Atangana–Baleanu Caputo derivative. The stability of the schemes is established numerically. Numerical examples are provided to support the theory presented in the paper. © 2018