An Efficient Technique for Coupled Fractional Whitham-Broer-Kaup Equations Describing the Propagation of Shallow Water Waves

Abstract

In the present work, the approximated analytical solution for the time-fractional coupled Whitham-Broer-Kaup (WBK) equations describing the propagation of shallow water waves are obtained with the aid of an efficient computational technique called, \( q \)-Homotopy analysis transform method (briefly, \( q \)-HATM). To demonstrate the reliability and efficiency of the proposed technique, two examples are illustrated. The homotopy polynomials are hired in order to handle the nonlinear terms and the suggested algorithm provides the auxiliary parameters \( \hbar \) and \( \fancyscript{n} \), which help us to control and adjust the convergence region of the obtained series solution. Numerical simulation has been carried out in terms of absolute error. The obtained results revels that, the proposed algorithm is highly methodical and very efficient to solve coupled nonlinear differential system.