{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T17:15:24Z","timestamp":1772644524721,"version":"3.50.1"},"reference-count":31,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T00:00:00Z","timestamp":1677024000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,3,15]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This work addresses existence and stabilization problem for a hybrid neutral stochastic delay differential equations with L\u00e9vy noise (HNSDDELN). The coefficients of such systems do not satisfy the conventional linear growth conditions, but are subject to high nonlinearity. We first prove the existence and uniqueness of the solution. We then design a delay feedback controller to make an unstable HNSDDELN $H_{\\infty }$ and asymptotically stable in ${\\mathbb{L}}^{p}$. We end up with a numerical example that corroborates our theoretical findings.<\/jats:p>","DOI":"10.1093\/imamci\/dnad002","type":"journal-article","created":{"date-parts":[[2023,2,23]],"date-time":"2023-02-23T07:19:03Z","timestamp":1677136743000},"page":"106-132","source":"Crossref","is-referenced-by-count":4,"title":["<i>H\u221e<\/i>and Asymptotic Stability via delay feedback for hybrid neutral stochastic delay differential equations with L\u00e9vy noise"],"prefix":"10.1093","volume":"40","author":[{"given":"Mohamed","family":"Rhaima","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University , P.O. Box 2455, Riyadh 11451 , Saudi Arabia"}]},{"given":"Lassaad","family":"Mchiri","sequence":"additional","affiliation":[{"name":"ENSIIE, University of Evry-Val-d\u2019Essonne , 1 square de la R\u00e9sistance 91000 \u00c9vry-Courcouronnes cedex , France"}]},{"given":"A","family":"Ben Makhlouf","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of sciences of Sfax, University of Sfax , Tunisia"}]}],"member":"286","published-online":{"date-parts":[[2023,2,22]]},"reference":[{"key":"2023031512451850500_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2021\/9444803","article-title":"A generalized definition of the fractional derivative with applications","volume":"2021","author":"Abu-Shady","year":"2021","journal-title":"Math. Probl. 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