{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T00:00:12Z","timestamp":1772755212031,"version":"3.50.1"},"reference-count":54,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2019,10,15]],"date-time":"2019-10-15T00:00:00Z","timestamp":1571097600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Thailand Research Grant Fund","award":["RSA5980019"],"award-info":[{"award-number":["RSA5980019"]}]},{"DOI":"10.13039\/501100009062","name":"Maejo University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100009062","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,9,16]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This manuscript prospects the controllability criteria of non-instantaneous impulsive Volterra type fractional differential systems. By enroling an appropriate Gramian matrix that is often defined by the Mittag-Leffler function and with the assistance of Laplace transform, the necessary and sufficiency conditions for the controllability of non-instantaneous impulsive Volterra-type fractional differential equations are derived by using algebraic approach and Cayley\u2013Hamilton theorem. An important feature present in our paper is that we have taken non-instantaneous impulses into the fractional order dynamical system and studied the controllability analysis, since this do not exist in the available source of literature. Inclusively, we have provided two illustrative examples with the existence of non-instantaneous impulse into the fractional dynamical system. So this demonstrates the validity and efficacy of our obtained criteria of the main section.<\/jats:p>","DOI":"10.1093\/imamci\/dnz025","type":"journal-article","created":{"date-parts":[[2019,8,15]],"date-time":"2019-08-15T19:12:44Z","timestamp":1565896364000},"page":"777-793","source":"Crossref","is-referenced-by-count":9,"title":["Controllability criteria of fractional differential dynamical systems with non-instantaneous impulses"],"prefix":"10.1093","volume":"37","author":[{"given":"B Sundara","family":"Vadivoo","sequence":"first","affiliation":[{"name":"Department of Mathematics, Alagappa University, Karaikudi 630004, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R","family":"Raja","sequence":"additional","affiliation":[{"name":"Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630 004, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinde","family":"Cao","sequence":"additional","affiliation":[{"name":"Research Center for Complex Systems and Network Sciences, School of Mathematics, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G","family":"Rajchakit","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aly R","family":"Seadawy","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Taibah University, Medina 41 477, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2019,10,15]]},"reference":[{"key":"2021060110091940500_ref1","first-page":"1","article-title":"Existence results for differential equations with fractional order and impulses","volume-title":"Mem. 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Theory Methods Appl."},{"key":"2021060110091940500_ref41","doi-asserted-by":"crossref","first-page":"599","DOI":"10.3390\/math7070599","article-title":"Robust synchronization of fractional-order uncertain chaotic systems based on output feedback sliding mode control","volume":"7","author":"Song","year":"2019","journal-title":"Mathematics"},{"key":"2021060110091940500_ref42","doi-asserted-by":"crossref","first-page":"2692","DOI":"10.1109\/TCSI.2012.2190573","article-title":"Pinning-controllability analysis of complex networks: an M-matrix approach","volume":"59","author":"Song","year":"2012","journal-title":"IEEE Trans. Circuits Systems I"},{"key":"2021060110091940500_ref43","doi-asserted-by":"crossref","DOI":"10.1155\/2015\/691687","article-title":"On stability of differential systems with noninstantaneous impulses","volume":"2015","author":"Sood","year":"2015","journal-title":"Math. Probl. 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