Abstract
In this study, I systematically investigate the fractional Whitham-Broer-Kaup (WBK) system and the fractional Coupled Jaulent-Miodek (CJM) equation under the Caputo fractional calculus. The nonlinear fractional differential equation systems are investigated via the Aboodh transform iteration method and the Aboodh residual power series method, thus offering a thorough analytical investigation. The dynamics of the fractional WBK system are accomplished using the Aboodh transform iteration method, and the Aboodh residual power series method is employed to study the behavior of the fractional CJM equation. Using established solutions, we completely analyze their dynamics employing both symbolic computations and numerical simulations. Consequently, novel solutions are identified, and the behavior of these fractional systems in the Caputo operator sense are clarified. The results obtained show good agreement of convergence of the numerical and analytical solutions, highlighting the effectiveness of the schemes adopted for unraveling the complex dynamics of fractional nonlinear systems.
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