Numerical approximation of fractional burgers equation with Atangana–Baleanu derivative in Caputo sense

Abstract

Abstract Burgers equation, a non-linear partial differential equation, occurs in many mathematical fields like fluid mechanics, gas dynamics, nonlinear acoustics, traffic flow, etc. This paper is based on a numerical technique using finite difference method to solve fractional Burgers equation. The fractional differential operator used here is Atangana-Baleanu fractional derivative whose kernel is a non-singular function. Some examples are considered to perform numerical simulations. The stability of the scheme is proved, and convergence is estimated numerically.