{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T04:09:44Z","timestamp":1768277384136,"version":"3.49.0"},"reference-count":41,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,1]],"date-time":"2023-07-01T00:00:00Z","timestamp":1688169600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11571136"],"award-info":[{"award-number":["11571136"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we study the averaging principle for \u03c8-Capuo fractional stochastic delay differential equations (FSDDEs) with Poisson jumps. Based on fractional calculus, Burkholder-Davis-Gundy\u2019s inequality, Doob\u2019s martingale inequality, and the Ho\u00a8lder inequality, we prove that the solution of the averaged FSDDEs converges to that of the standard FSDDEs in the sense of Lp. Our result extends some known results in the literature. Finally, an example and simulation is performed to show the effectiveness of our result.<\/jats:p>","DOI":"10.3390\/sym15071346","type":"journal-article","created":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T00:34:08Z","timestamp":1688344448000},"page":"1346","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Averaging Principle for \u03c8-Capuo Fractional Stochastic Delay Differential Equations with Poisson Jumps"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8056-6973","authenticated-orcid":false,"given":"Dandan","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Huaiyin Normal University, Huaian 223300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingfeng","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Huaiyin Normal University, Huaian 223300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuanzhi","family":"Bai","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Huaiyin Normal University, Huaian 223300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2017.05.005","article-title":"Symmetry of stochastic non-variational differential equations","volume":"686","author":"Gaeta","year":"2017","journal-title":"Phys. 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