An Analysis of the Nonlinear Time-Fractional Schrödinger and Coupled Klein–Gordon–Schrödinger Equations

In this study, the fractional Schrödinger and the coupled Klein–Gordon–Schrödinger equations are investigated using the Caputo fractional operator. The homotopy analysis [Formula: see text]-transform method is implemented to investigate the solution of time-fractional nonlinear Schrödinger and coupled Klein–Gordon–Schrödinger equations. The convergence of the proposed method is examined with the help of the Banach approach. The proposed technique effectively derives the approximate solution of the time-fractional Schrödinger and coupled Klein–Gordon–Schrödinger equations. The current framework precisely depicts the behavior of the attained results for different fractional orders. Graphical representations and numerical results precisely demonstrate the effectiveness and reliability of the proposed method.