On the Solutions of the Fractional-Order Sawada–Kotera–Ito Equation and Modeling Nonlinear Structures in Fluid Mediums

This study investigates the wave solutions of time-fractional Sawada–Kotera–Ito equation (SKIE) that arise in shallow water and many other fluid mediums by utilizing some most flexible high-precision methods. The SKIE is a nonlinear integrable partial differential (PDE) with significant applications dynamics mechanics. However, traditional numerical methods used for analyzing this are often plagued difficulties handling fractional derivatives (FDs), which lead to finding techniques overcome these difficulties. To address challenge, Adomian decomposition (AD) transform method (ADTM) homotopy perturbation (HPTM) employed obtain exact SKIE. ADTM involves decomposing into series polynomials solving each component iteratively. HPTM modified uses continuous deformation known solution desired solution. results show both can produce accurate stable In addition, we compare obtained from demonstrate superiority terms efficiency accuracy. provides valuable insights waves plasma, has important implications equations (FPDEs). conclusion, offers effective efficient demonstrates their usefulness PDEs.