The novel conformable methods to solve conformable time- fractional coupled Whitham-Broer-Kaup equation

This study employs two innovative techniques, namely the conformable q-homotopy analysis transform method (Cq-HATM) and the conformable Elzaki Adomian decomposition method (CEADM), to investigate the numerical solutions for the conformable time-fractional coupled Whitham-Broer-Kaup problem. One of the two novel approaches offered is Cq-HATM, which is a hybrid approach that integrates the q-homotopy analysis transform method with Laplace transform using the concept of conformable derivative. The CEADM method, like the aforementioned approach, is a hybrid method that integrates the Adomian decomposition method and Elzaki transform by utilizing the concept of conformable derivative. The computer simulations were conducted in order to provide empirical evidence supporting the efficacy and reliability of the recommended methodologies. Upon comparing the precise solutions with the obtained solutions, it becomes evident that both of the novel methodologies exhibit simplicity, efficacy, and proficiency in addressing nonlinear conformable time-fractional partial differential equations.