Investigation of fractal fractional nonlinear Korteweg-de-Vries-Schrödinger system with power law kernel

Abstract

In this research article, we invetsigate the Schrödinger-KdV equation under Caputo fractal fractional (FF) operator. We analyze and prove the existence, uniqueness and convergence of the solution via fixed point theory and nonlinear functional analysis. We apply the Yang transform homotopy perturbation method (YTHPM) to solve the Schrödinger-KdV equation with Caputo FF operator. Using the YTHPM, we derive an approximate solution to the Schrödinger-KdV equation and provide graphical representations of the result to showcase the behaviour of solution for various sets of fractional and fractal orders. Our findings and error analysis demonstrate that the YTHPM and the Caputo fractal-fractional operator are effective in solving the Schrödinger-KdV equation.