Theoretical and Computational Insights into a System of Time-Fractional Nonlinear Schrödinger Delay Equations
This research focuses on the theoretical asymptotic stability and long-time decay of the zero solution for a system of time-fractional nonlinear Schrödinger delay equations (NSDEs) in the context of the Caputo fractional derivative. Using the fractional Halanay inequality, we demonstrate theoretical...
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MDPI AG
2025-06-01
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| author | Mai N. Elhamaky Mohamed A. Abd Elgawad Zhanwen Yang Ahmed S. Rahby |
| author_facet | Mai N. Elhamaky Mohamed A. Abd Elgawad Zhanwen Yang Ahmed S. Rahby |
| author_sort | Mai N. Elhamaky |
| collection | DOAJ |
| description | This research focuses on the theoretical asymptotic stability and long-time decay of the zero solution for a system of time-fractional nonlinear Schrödinger delay equations (NSDEs) in the context of the Caputo fractional derivative. Using the fractional Halanay inequality, we demonstrate theoretically when the considered system decays and behaves asymptotically, employing an energy function in the sense of the <i>L</i><sub>2</sub> norm. Together with utilizing the finite difference method for the spatial variables, we investigate the long-time stability for the semi-discrete system. Furthermore, we operate the L1 scheme to approximate the Caputo fractional derivative and analyze the long-time stability of the fully discrete system through the discrete energy of the system. Moreover, we demonstrate that the proposed numerical technique energetically captures the long-time behavior of the original system of NSDEs. Finally, we provide numerical examples to validate the theoretical results. |
| format | Article |
| id | doaj-art-94b01031dbdb49709187ae8a44319d6e |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-94b01031dbdb49709187ae8a44319d6e2025-08-20T02:24:18ZengMDPI AGAxioms2075-16802025-06-0114643210.3390/axioms14060432Theoretical and Computational Insights into a System of Time-Fractional Nonlinear Schrödinger Delay EquationsMai N. Elhamaky0Mohamed A. Abd Elgawad1Zhanwen Yang2Ahmed S. Rahby3School of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaSchool of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Faculty of Science, Benha University, Benha 13518, EgyptThis research focuses on the theoretical asymptotic stability and long-time decay of the zero solution for a system of time-fractional nonlinear Schrödinger delay equations (NSDEs) in the context of the Caputo fractional derivative. Using the fractional Halanay inequality, we demonstrate theoretically when the considered system decays and behaves asymptotically, employing an energy function in the sense of the <i>L</i><sub>2</sub> norm. Together with utilizing the finite difference method for the spatial variables, we investigate the long-time stability for the semi-discrete system. Furthermore, we operate the L1 scheme to approximate the Caputo fractional derivative and analyze the long-time stability of the fully discrete system through the discrete energy of the system. Moreover, we demonstrate that the proposed numerical technique energetically captures the long-time behavior of the original system of NSDEs. Finally, we provide numerical examples to validate the theoretical results.https://www.mdpi.com/2075-1680/14/6/432system of time-fractional nonlinear Schrödinger equationstime delaylong-time stabilityfractional halanay inequalityL1-finite difference method |
| spellingShingle | Mai N. Elhamaky Mohamed A. Abd Elgawad Zhanwen Yang Ahmed S. Rahby Theoretical and Computational Insights into a System of Time-Fractional Nonlinear Schrödinger Delay Equations Axioms system of time-fractional nonlinear Schrödinger equations time delay long-time stability fractional halanay inequality L1-finite difference method |
| title | Theoretical and Computational Insights into a System of Time-Fractional Nonlinear Schrödinger Delay Equations |
| title_full | Theoretical and Computational Insights into a System of Time-Fractional Nonlinear Schrödinger Delay Equations |
| title_fullStr | Theoretical and Computational Insights into a System of Time-Fractional Nonlinear Schrödinger Delay Equations |
| title_full_unstemmed | Theoretical and Computational Insights into a System of Time-Fractional Nonlinear Schrödinger Delay Equations |
| title_short | Theoretical and Computational Insights into a System of Time-Fractional Nonlinear Schrödinger Delay Equations |
| title_sort | theoretical and computational insights into a system of time fractional nonlinear schrodinger delay equations |
| topic | system of time-fractional nonlinear Schrödinger equations time delay long-time stability fractional halanay inequality L1-finite difference method |
| url | https://www.mdpi.com/2075-1680/14/6/432 |
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