New Soliton Solutions of Time-Fractional Korteweg–de Vries Systems

Model construction for different physical situations, and developing their solutions, are the major characteristics of scientific work in physics engineering. Korteweg–de Vries (KdV) models very important due to ability capture situations such as thin film flows waves on shallow water surfaces. In this work, a new approach predicting analyzing nonlinear time-fractional coupled KdV systems is proposed based Laplace transform homotopy perturbation along with Caputo fractional derivatives. This algorithm provides convergent series solution by applying simple steps through symbolic computations. The efficiency tested against systems, including dispersive long wave generalized Hirota–Satsuma systems. For validity purposes, obtained results compared existing solutions from literature. convergence over entire domain confirmed finding errors at various values parameters. Numerical simulations clearly reassert supremacy capability technique terms accuracy fewer computations other available schemes. Analysis reveals that projected scheme reliable hence can be utilized kernels more advanced