Efficient numerical approach for solving fractional partial differential equations with non-singular kernel derivatives

Adams-Bashforth was recognized as powerful numerical method to solve linear and non-linear ordinary differential equations. Nevertheless the method was applicable only for ordinary differential equations mostly with integer order. Atangana and Batogna have extended this method for partial differential equation with the Atangana-Baleanu fractional derivative. In this paper, to accommodate partial differential equation with Caputo-Fabrizio derivative, we suggest the corresponding method with this derivative. We applied the method to solve numerically a very interesting non-linear partial differential equation accounting for the motion of a viscous fluid. Some simulations are presented to test the efficiency of the numerical method.