ANALYSIS OF THE NONLINEAR FRACTIONAL BENNEY EQUATION WITH NON-SINGULAR DERIVATIVE

In this work, we introduce a new method for applying the Laplace Adomian decomposition method (LADM) to solve the Benney problem within the Atangana–Baleanu–Caputo (ABC) derivative framework. We provide a strong theoretical basis by carefully proving the existence and uniqueness of solutions. Our novel method offers a thorough solution process, which is graphically represented by a sequence of three- and two-dimensional plots that clearly depict the numerical solutions. This research also serves to provide a more holistic insight into the analytical understanding of Benney’s equation. It shows the flexibility and strength of LADM in solving complex mathematical problems, opening new avenues for future research in fluid flow, propagation of waves, and nonlinear systems.