Sumudu decomposition method with non-singular kernel operators for solving time fractional Whitham-Broer-Kaup equations

This paper presents an analytical solution framework for the coupled fractional Whitham–Broer–Kaup (FWBK) equations using the Sumudu transform (ST) and decomposition method (DM), where the fractional derivatives of Atangana–Baleanu in Caputo sense (ABC) and Caputo–Fabrizio (CF) are utilized throughout the paper. The FWBK system describes nonlinear shallow water wave propagation and has conventionally been treated using classical fractional operators such as the Caputo or Atangana-Baleanu derivatives together with Laplace-type or natural integral transforms and iterative techniques. By reducing the solution process and with keeping of both initial and boundary conditions, ST is used as a powerful analytical tool. We show that our approach is accurate and convergence by proving exact and approximate solutions for FWBK equations. A detailed comparison with other methods confirms that the SDM framework is simple to implement and physically sound. This work helps for progressing the fractional modelling and to fill the gap of non-singular fractional calculus with integral transform methods, providing a new point of view in solving the complex nonlinear fractional PDEs. Both numerical and graphical results show that the present method is very accurate and simple in analysing and solving the fractionally linked nonlinear complex problems appearing in science and technology.