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Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative <jats:italic>U<\/jats:italic>-controllability are established and proved. Numerical examples illustrate the obtained theoretical results.<\/jats:p>","DOI":"10.1515\/amcs-2016-0036","type":"journal-article","created":{"date-parts":[[2016,9,30]],"date-time":"2016-09-30T07:47:30Z","timestamp":1475221650000},"page":"521-531","source":"Crossref","is-referenced-by-count":11,"title":["Controllability criteria for time\u2013delay fractional systems with a retarded state"],"prefix":"10.61822","volume":"26","author":[{"given":"Beata","family":"Sikora","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"37438","published-online":{"date-parts":[[2016,9,29]]},"reference":[{"key":"2021040810592397589_j_amcs-2016-0036_ref_001_w2aab2b8c16b1b7b1ab1ab1Aa","unstructured":"Babiarz, A., Grzejszczak, T., \u0141egowski, A. and Niezabitowski, M. (2016). 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