Investigation of the fractional coupled viscous Burgers' equation involving Mittag-Leffler kernel.

This study investigates the fractional coupled viscous Burgers' equation under the Liouville–Caputo, Atangana–Baleanu and Yang–Srivastava–Machado fractional derivatives. With the help of fixed-point theorem, and using the Atangana–Baleanu fractional derivative with Mittag-Leffler kernel type kernel, we proved the existence and uniqueness of the studied model. The Laplace Homotopy perturbation method (LPM) defined with the Liouville–Caputo, Atangana–Baleanu and Yang–Srivastava–Machado operators is used in obtaining the exact solutions of the nonlinear model. The numerical simulations of the obtained solutions are performed. We have seen the effect of the various parameters and variables on the displacement in Figs. 1–6. • A nonlinear fractional model is investigated. • The closed form solution to the nonlinear fractional model is obtained. • Using the fixed-point theorem, the existence and uniqueness of the solution are analyzed. • The numerical simulations to the obtained solution are presented. [ABSTRACT FROM AUTHOR]