Analytical Approaches for Approximate Solution of the Time-Fractional Coupled Schrödinger–KdV Equation

In this article, we use the homotopy perturbation method and the Adomian decomposition method with the Yang transformation to discover analytical solution to the time-fractional coupled Schrödinger–KdV equation. In the Caputo sense, fractional derivatives are described. A convergent series is used to calculate the solutions of fractional PDEs. Analytical results achieved applying the homotopy perturbation and decomposition techniques are numerically calculated and represented in the form of tables and figures. The simplicity, efficacy, and high degree of accuracy of the used method are then demonstrated by comparing these solutions to the actual solutions and the results. Finally, the applied approaches are the most popular and convergent methods for solving nonlinear fractional-order partial deferential problems.