Abstract.

This article presents a new approach so-called the Laplace-residual power series method (L-RPSM) for estimating the solution of a coupled system of fractional partial differential equation (FPDE). To demonstrate the efficiency of the L-RPSM, we found the solution of the time-fractional Whitham-Broer-Kaup (WBK) equations, where the derivative is given in the Liouville-Caputo sense. A comparison of the numerical results obtained using our method and the results obtained using Adomian decomposition method (ADM), Variational iteration method (VIM), Optimal homotopy asymptotic method (OHAM), Daftardar-Gejji and Jafari method (DJM) and Laplace transform Adomian decomposition method (LADM) is given. Consequently the results show that the L-RPSM is reliable and effective for solving coupled systems of the FPDE. Moreover, the solutions obtained by the L-RPSM converge faster than the solutions obtained using ADM, VIM, OHAM, DJM and LADM to the exact solution.

Keywords:

Liouville-Caputo, fractional derivative operator, Laplace-Residual, power series, Whitham-Broer-Kaup equations.