Numerical Solutions of Time-Fractional Whitham–Broer–Kaup Equations via Sumudu Decomposition Method

In this paper, the coupled system of Whitham–Broer–Kaup equations of the Caputo fractional derivative (CFD) is studied using
the Sumudu decomposition method (SDM). Using di9erent dispersion relations, these equations are needed to describe the
properties of waves in shallow water. (e current investigation for the future scheme includes convergence and error analysis. We
use two examples to demonstrate the leverage and e9ectiveness of the proposed scheme, and the error analysis is discussed to
ensure its accuracy. (e numerical simulation is carried out to ensure the accuracy of the future technique. (e obtained
numerical and graphical results are presented, and the proposed scheme is computationally very accurate and simple to study and
solve fractionally coupled nonlinear complex phenomena encountered in science and technology.