Investigating the Dynamics of Time-Fractional Drinfeld–Sokolov–Wilson System through Analytical Solutions

This study addresses a nonlinear fractional Drinfeld–Sokolov–Wilson problem in dispersive water waves, which requires appropriate numerical techniques to obtain an approximative solution. The Adomian decomposition approach, the homotopy perturbation method, and Sumudu transform are combined tackle problem. Caputo manner is used describe derivative, He’s polynomials employed address nonlinearity. By following these approaches, we solutions form of convergent series. We verify demonstrate effectiveness our suggested strategies by examining assumed model terms order. use plots for various orders represent physical behavior technique solutions, show simulation. results that algorithms systematic, simple use, effective, accurate analyzing coupled differential equations order related scientific engineering fields.