Numerical simulation of coupled fractional-order Whitham-Broer-Kaup equations arising in shallow water with Atangana-Baleanu derivative

In this manuscript, fractional nonlinear coupled Whitham-Broer-Kaup equation associated with Atangana-Baleanu fractional derivative is considered. General conditions under which a system solution exists and is unique are presented using the fixed-point theorem method. For numerical simulations, coupled fractional modified Boussinesq equations and coupled fractional approximate long wave equations are investigated using the homotopy perturbation transform technique (HPTT). The suggested technique is an elegant compilation of the Laplace transform technique with the homotopy perturbation approach. The physical behavior of the obtained solutions has been presented graphically as well as in tables for diverse fractional order. Comparative simulations have been performed to validate the efficiency and accuracy of the suggested technique.