Approximate analytical solutions of fractional coupled Whitham-Broer-Kaup equations via novel transform

In this study, 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, homotopy analysis Shehu transform methodm(briefly, HASTM). The Caputo operator is utilized to describe fractional-order derivatives. Our proposed approach combines the Shehu transformation with the homotopy analysis method, employing homotopy polynomials to handle nonlinear terms. To validate the correctness of our method, we offer a comparison of obtained and exact solutions with different fractional order values. Given its novelty and straightforward implementation, our method is considered a reliable and efficient analytical technique for solving both linear and non-linear fractional partial differential equations.