Fractional View Analysis of Coupled Whitham-Broer-Kaup Equations Arising in Shallow Water with Caputo Derivative

Abstract

This research explores the analysis of the nonlinear fractional systems described by the Whitham-Broer-Kaup equations using novel mathematical tools like the Aboodh transform iteration method and the Aboodh residual power series method in light of the Caputo operator theory. The Whitham-Broer-Kaup equations are critical for describing the nonlinear propagation of dispersive waves and have enormous practical relevance. In the application of the Aboodh transform iteration method and the Aboodh residual power series method, as well as the introduction of the Caputo operator, the modelling accuracy is improved by calculating the fractional derivatives. The study has proven the usefulness of these techniques in providing solutions to fractional nonlinear systems that are only approximate but are insightful concerning dynamic behaviour. The insertion of the Caputo operator in the modelling method gives it some sophistication, simulating the non-locality inherent in fractional calculus. Consequently, this study enriches mathematical models and computational approaches, bringing in solid tools for researchers who want to examine complex nonlinear systems with fractional nature.