Fractional generalized perturbed KdV equation with a power Law kernel: A computational study

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In this study, we analyze the nonlinear generalized perturbed KdV equation using the Shehu transform and decomposition approach to obtain solutions. Multiple cases with appropriate initial conditions demonstrate the procedure’s effectiveness and validity, with excellent agreements noted. Simulations reveal three distinct solutions: one bright-soliton, two wave solutions, and dark-bright soliton solutions. Fractional order significantly impacts wave amplitudes and nonlinearity characteristics, affecting system excitations. These findings offer insights into complex behaviors, with potential applications in fluid dynamics, nonlinear optics, and plasma physics, guiding experimental design and system analysis.