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<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2457_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(L1\)</EquationSource> </InlineEquation> 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.</p>

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Theoretical and numerical aspects for long-time behavior of multidimensional time-fractional Schrödinger equations with delay

  • 期刊论文

  • 发表日期：

    2025年4月18日

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  • Mai N. Elhamaky,
  • Minghui Song

摘要

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 \(L1\) 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.