{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T03:37:58Z","timestamp":1778211478475,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,14]],"date-time":"2024-12-14T00:00:00Z","timestamp":1734134400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Technological Development, Republic of Serbia","award":["174024"],"award-info":[{"award-number":["174024"]}]},{"name":"bilateral project between MANU and SANU","award":["174024"],"award-info":[{"award-number":["174024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The study of long-term behavior in stochastic systems is critical for understanding the dynamics of complex processes influenced by randomness. This paper addresses the existence and uniqueness of Stepanov-like pseudo S-asymptotically (\u03c9,c)-periodic solutions for a class of stochastic integro-differential equations. These equations model systems where the interplay between deterministic and stochastic components dictates the overall dynamics, making periodic analysis essential. The problem addressed in this study is the lack of a comprehensive framework to describe the periodic behavior of such systems in noisy environments. To tackle this, we employ advanced techniques in stochastic analysis, fixed-point theorems and the properties of L1- and L2-convolution kernels to establish conditions for the existence and uniqueness of mild solutions under these extended periodicity settings. The methodology involves leveraging the decay properties of the operator kernels and the boundedness of stochastic integrals to ensure well-posedness. The major outputs of this study include novel results on the existence, uniqueness and stability of Stepanov-like pseudo S-asymptotically (\u03c9,c)-periodic solutions, along with illustrative example demonstrating their applicability in real-world stochastic systems.<\/jats:p>","DOI":"10.3390\/axioms13120871","type":"journal-article","created":{"date-parts":[[2024,12,17]],"date-time":"2024-12-17T06:26:12Z","timestamp":1734416772000},"page":"871","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Stepanov-like Pseudo S-Asymptotically (\u03c9, c)-Periodic Solutions of a Class of Stochastic Integro-Differential Equations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0392-4976","authenticated-orcid":false,"given":"Marko","family":"Kosti\u0107","sequence":"first","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovi\u0107a 6, 21125 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8880-1552","authenticated-orcid":false,"given":"Halis Can","family":"Koyuncuo\u011flu","sequence":"additional","affiliation":[{"name":"Department of Engineering Sciences, Faculty of Engineering and Architecture, Izmir Katip Celebi University, 35620 Izmir, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,14]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Existence of almost periodic solutions for semilinear stochastic evolution equations driven by fractional Brownian motion","volume":"2012","author":"Bezandry","year":"2012","journal-title":"Electron. J. Differ. Equ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.14232\/ejqtde.2008.1.35","article-title":"Existence of S2\u2013almost periodic solutions to a class of nonautonomous stochastic evolution equation","volume":"35","author":"Bezandry","year":"2008","journal-title":"Electron. J. Qual. Theory Differ. Equ."},{"key":"ref_3","unstructured":"Zhao, S., and Song, M. (2016). 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