{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:21:21Z","timestamp":1760059281411,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T00:00:00Z","timestamp":1748736000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This research focuses on the theoretical asymptotic stability and long-time decay of the zero solution for a system of time-fractional nonlinear Schr\u00f6dinger 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 L2 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.<\/jats:p>","DOI":"10.3390\/axioms14060432","type":"journal-article","created":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T10:21:49Z","timestamp":1748859709000},"page":"432","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Theoretical and Computational Insights into a System of Time-Fractional Nonlinear Schr\u00f6dinger Delay Equations"],"prefix":"10.3390","volume":"14","author":[{"given":"Mai N.","family":"Elhamaky","sequence":"first","affiliation":[{"name":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9540-9439","authenticated-orcid":false,"given":"Mohamed A.","family":"Abd Elgawad","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}]},{"given":"Zhanwen","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1103-3652","authenticated-orcid":false,"given":"Ahmed S.","family":"Rahby","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,1]]},"reference":[{"key":"ref_1","unstructured":"Berezin, F.A., and Shubin, M. 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