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By elaborating the rank criterion and the conformable Gram criterion, sufficient and necessary conditions to investigate that a linear general conformable system is null completely controllable are given. We obtain a full generalization to the general conformable fractional\u2010order system case. In addition, Krasnoselskii\u2019s fixed point theorem to obtain a complete controllability result for a semilinear general conformable system is applied.<\/jats:p>","DOI":"10.1155\/2021\/2817092","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T22:12:11Z","timestamp":1633990331000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Controllability of Differential Systems with the General Conformable Derivative"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5417-6277","authenticated-orcid":false,"given":"Ferrag","family":"Azouz","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7619-8584","authenticated-orcid":false,"given":"Djalal","family":"Boucenna","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7142-7026","authenticated-orcid":false,"given":"Abdellatif","family":"Ben Makhlouf","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3704-1845","authenticated-orcid":false,"given":"Lassaad","family":"Mchiri","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6954-5090","authenticated-orcid":false,"given":"Abbes","family":"Benchaabane","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,10,11]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"crossref","unstructured":"DadrasS.andMomeniH. 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