We address in this study the theoretical asymptotic stability and long-time decay for the zero solution of the multidimensional time-fractional Schrödinger equations (TFSEs) with delay using the Fractional Halanay inequality. Besides employing the central finite difference scheme for spatial discretization, the
scheme is utilized to approximate the Caputo fractional derivative. Additionally, we investigate the solvability of numerical scheme. It is shown that the long-time behavior of the original problems may be accurately represented by the numerical method. Lastly, the theoretical approach is supported by numerical examples that agree with these results. |
