{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T21:39:28Z","timestamp":1782250768976,"version":"3.54.5"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T00:00:00Z","timestamp":1762905600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science and Technology Council of the Republic of China","award":["NSTC 113-2115-M-017-004"],"award-info":[{"award-number":["NSTC 113-2115-M-017-004"]}]},{"name":"National Science and Technology Council of the Republic of China","award":["NSTC 114-2115-M-017-002"],"award-info":[{"award-number":["NSTC 114-2115-M-017-002"]}]},{"name":"Ministry of Science and Technological Development, Republic of Serbia","award":["174024"],"award-info":[{"award-number":["174024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper investigates the existence of square-mean S-asymptotically (\u03c9,c)-periodic solutions for a class of neutral impulsive stochastic differential equations driven by fractional Brownian motion, addressing the challenge of modeling long-range dependencies, delayed feedback, and abrupt changes in systems like biological networks or mechanical oscillators. By employing semigroup theory to derive mild solution representations and the Banach contraction principle, we establish sufficient conditions\u2013such as Lipschitz continuity of nonlinear terms and growth bounds on the resolvent operator\u2014that guarantee the uniqueness and existence of such solutions in the space SAP\u03c9,c([0,\u221e),L2(\u03a9,H)). The important results demonstrate that under these assumptions, the mild solution exhibits square-mean S-asymptotic (\u03c9,c)-periodicity, enabling robust asymptotic analysis beyond classical periodicity. We illustrate these findings with examples, such as a neutral stochastic heat equation with impulses, revealing stability thresholds and decay rates and highlighting the framework\u2019s utility in predicting long-term dynamics. These outcomes advance stochastic analysis by unifying neutral, impulsive, and fractional noise effects, with potential applications in control theory and engineering.<\/jats:p>","DOI":"10.3390\/sym17111938","type":"journal-article","created":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T10:56:47Z","timestamp":1762945007000},"page":"1938","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Square-Mean S-Asymptotically (\u03c9,c)-Periodic Solutions to Neutral Stochastic Impulsive Equations"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8612-6100","authenticated-orcid":false,"given":"Belkacem","family":"Chaouchi","sequence":"first","affiliation":[{"name":"National Higher School of Cybersecurity, Mahelma 16093, Algeria"},{"name":"Laboratory of Energy and Intelligent Systems, Khemis Miliana University, Khemis Miliana 11000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8996-2270","authenticated-orcid":false,"given":"Wei-Shih","family":"Du","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824004, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0392-4976","authenticated-orcid":false,"given":"Marko","family":"Kosti\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovi\u0107a 6, 21125 Novi Sad, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8811-4288","authenticated-orcid":false,"given":"Daniel","family":"Velinov","sequence":"additional","affiliation":[{"name":"Department for Mathematics and Informatics, Faculty of Civil Engineering, Ss. Cyril and Methodius University in Skopje, Partizanski Odredi 24, P.O. Box 560, 1000 Skopje, North Macedonia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,12]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"(\u03c9,c)-periodic functions and mild solutions to abstract fractional integro-differential equations","volume":"18","author":"Alvarez","year":"2018","journal-title":"Electron. J. Differ. 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