{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T01:28:50Z","timestamp":1773451730095,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,9]],"date-time":"2022-12-09T00:00:00Z","timestamp":1670544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basque Government","award":["IT1155-22"],"award-info":[{"award-number":["IT1155-22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The study of dynamic systems appears in various aspects of dynamical structures such as decomposition, decoupling, observability, and controllability. In the present research, we study the controllability of fractional stochastic systems (FSF) and examine the Poisson jumps in finite dimensional space where the fractional impulsive neutral stochastic system is controllable. Sufficient conditions are demonstrated with the aid of fixed point theory. The Mittag-Leffler (ML) matrix function defines the controllability of the Grammian matrix (GM). The relation to symmetry is clear since the controllability Grammian is a hermitian matrix (since the integrand in its definition is hermitian) and this is the complex version of a symmetric matrix. In fact, such a Grammian becomes a symmetric matrix in the specific scenario where the controllability Grammian is a real matrix. Some examples are provided to demonstrate the feasibility of the present theory.<\/jats:p>","DOI":"10.3390\/sym14122612","type":"journal-article","created":{"date-parts":[[2022,12,9]],"date-time":"2022-12-09T04:46:46Z","timestamp":1670561206000},"page":"2612","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Controllability of Impulsive Neutral Fractional Stochastic Systems"],"prefix":"10.3390","volume":"14","author":[{"given":"Qura Tul","family":"Ain","sequence":"first","affiliation":[{"name":"Department of Mathematics, Guizhou University, Guizhou 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9349-4729","authenticated-orcid":false,"given":"Muhammad","family":"Nadeem","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9832-1424","authenticated-orcid":false,"given":"Ali","family":"Akg\u00fcl","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Mathematics, Lebanese American University,  Beirut 1102 2801, Lebanon"},{"name":"Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey"},{"name":"Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, Mersin 10, 99138 Nicosia, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel","family":"De la Sen","sequence":"additional","affiliation":[{"name":"Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science, Technology University of the Basque Country, 48940 Leioa, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/BF00938943","article-title":"Controllability of nonlinear systems via fixed-point theorems","volume":"53","author":"Balachandran","year":"1987","journal-title":"J. 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