{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:16:17Z","timestamp":1772295377119,"version":"3.50.1"},"reference-count":33,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"3","license":[{"start":{"date-parts":[[2017,9,1]],"date-time":"2017-09-01T00:00:00Z","timestamp":1504224000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper is concerned with the controllability of nonlinear fractional delay dynamical systems with implicit fractional derivatives for multiple delays and distributed delays in control variables. Sufficient conditions are obtained by using the Darbo fixed point theorem. Further, examples are given to illustrate the theory.<\/jats:p>","DOI":"10.1515\/amcs-2017-0035","type":"journal-article","created":{"date-parts":[[2017,9,25]],"date-time":"2017-09-25T10:00:43Z","timestamp":1506333643000},"page":"501-513","source":"Crossref","is-referenced-by-count":7,"title":["The controllability of nonlinear implicit fractional delay dynamical systems"],"prefix":"10.61822","volume":"27","author":[{"given":"Rajagopal","family":"Joice Nirmala","sequence":"first","affiliation":[{"name":"Department of Mathematics , Bharathiar University , Coimbatore 641 046 , India"}]},{"given":"Krishnan","family":"Balachandran","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Bharathiar University , Coimbatore 641 046 , India"}]}],"member":"37438","published-online":{"date-parts":[[2017,9,23]]},"reference":[{"key":"2021040723004707401_j_amcs-2017-0035_ref_001_w2aab3b7b4b1b6b1ab1ab1Aa","unstructured":"Adams, J. and Hartley, T. (2008). Finite time controllability of fractional order systems, Journal of Computational and Nonlinear Dynamics3(2): 1\u20135.10.1115\/1.2833919"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_002_w2aab3b7b4b1b6b1ab1ab2Aa","unstructured":"Balachandran, K. (1988). Controllability of nonlinear systems with implicit derivatives, IMA Journal of Mathematical Control and Information5(2): 77\u201383.10.1093\/imamci\/5.2.77"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_003_w2aab3b7b4b1b6b1ab1ab3Aa","unstructured":"Balachandran, K. (1989). Controllability of nonlinear delay systems with an implicit derivative, International Journal of Control50(4): 1525\u20131531.10.1080\/00207178908953444"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_004_w2aab3b7b4b1b6b1ab1ab4Aa","unstructured":"Balachandran, K. and Divya, S. (2014). Controllability of nonlinear implicit fractional integrodifferential systems, International Journal of Applied Mathematics and Computer Science24(4): 713\u2013722, DOI: 10.2478\/amcs-2014-0052.10.2478\/amcs-2014-0052"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_005_w2aab3b7b4b1b6b1ab1ab5Aa","unstructured":"Balachandran, K. and Kokila, J. (2012). On the controllability of fractional dynamical systems, International Journal of Applied Mathematics and Computer Science22(3): 523\u2013531, DOI: 10.2478\/v10006-012-0039-0.10.2478\/v10006-012-0039-0"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_006_w2aab3b7b4b1b6b1ab1ab6Aa","unstructured":"Balachandran, K. and Kokila, J. (2014). Controllability of non-linear implicit fractional dynamical systems, IMA Journal of Applied Mathematics79(7): 562\u2013570.10.1093\/imamat\/hxt003"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_007_w2aab3b7b4b1b6b1ab1ab7Aa","doi-asserted-by":"crossref","unstructured":"Balachandran, K., Kokila, J. and Trujillo, J. (2012a). Relative controllability of fractional dynamical systems with multiple delays in control, Computer and Mathematics with Applications64(10): 3037\u20133045.","DOI":"10.1016\/j.camwa.2012.01.071"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_008_w2aab3b7b4b1b6b1ab1ab8Aa","doi-asserted-by":"crossref","unstructured":"Balachandran, K., Park, J. and Trujillo, J. (2012b). Controllability of nonlinear fractional dynamical systems, Nonlinear Analysis75(4): 1919\u20131926.","DOI":"10.1016\/j.na.2011.09.042"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_009_w2aab3b7b4b1b6b1ab1ab9Aa","unstructured":"Balachandran, K. and Somasundaram, D. (1983). Controllability of a class of nonlinear systems with distributed delays in control, Kybernetika19(6): 475\u2013481."},{"key":"2021040723004707401_j_amcs-2017-0035_ref_010_w2aab3b7b4b1b6b1ab1ac10Aa","unstructured":"Balachandran, K. and Somasundaram, D. (1986). Controllability of nonlinear delay systems with delay depending on state variable, Kybernetika22(5): 439\u2013444."},{"key":"2021040723004707401_j_amcs-2017-0035_ref_011_w2aab3b7b4b1b6b1ab1ac11Aa","doi-asserted-by":"crossref","unstructured":"Balachandran, K., Zhou, Y. and Kokila, J. (2012c). Relative controllability of fractional dynamical system with distributed delay in control, Computer and Mathematics with Applications64(10): 3201\u20133209.","DOI":"10.1016\/j.camwa.2011.11.061"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_012_w2aab3b7b4b1b6b1ab1ac12Aa","doi-asserted-by":"crossref","unstructured":"Bellman, R. and Cooke, K. (1963). Differential-Difference Equations, Academic Press, New York, NY.","DOI":"10.1063\/1.3050672"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_013_w2aab3b7b4b1b6b1ab1ac13Aa","doi-asserted-by":"crossref","unstructured":"Bettayeb, M. and Djennoune, S. (2008). New results on the controllability of fractional dynamical systems, Journal of Vibrating and Control14(9): 1531\u20131541.","DOI":"10.1177\/1077546307087432"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_014_w2aab3b7b4b1b6b1ab1ac14Aa","doi-asserted-by":"crossref","unstructured":"Bhalekar, S. and Gejji, V. (2010). Fractional ordered Liu system with time-delay, Communication in Nonlinear Sciences and Numerical Simulation15(8): 2178\u20132191.","DOI":"10.1016\/j.cnsns.2009.08.015"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_015_w2aab3b7b4b1b6b1ab1ac15Aa","doi-asserted-by":"crossref","unstructured":"Bhalekar, S., Gejji, V., Baleanu, D. and Magin, R. (2011). Fractional Bloch equation with delay, Computer and Mathematics with Applications61(5): 1355\u20131365.","DOI":"10.1016\/j.camwa.2010.12.079"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_016_w2aab3b7b4b1b6b1ab1ac16Aa","unstructured":"Dacka, C. (1980). On the controllability of a class of nonlinear systems, IEEE Transactions on Automatic Control25(2): 263\u2013266.10.1109\/TAC.1980.1102287"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_017_w2aab3b7b4b1b6b1ab1ac17Aa","unstructured":"Dacka, C. (1982). Relative controllability of perturbed nonlinear systems with delay in control, IEEE Transactions on Automatic Control27(1): 268\u2013270.10.1109\/TAC.1982.1102846"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_018_w2aab3b7b4b1b6b1ab1ac18Aa","doi-asserted-by":"crossref","unstructured":"Dauer, J. and Gahl, R. (1977). Controllability of nonlinear delay systems, Journal of Optimization Theory and Applications21(1): 59\u201370.","DOI":"10.1007\/BF00932544"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_019_w2aab3b7b4b1b6b1ab1ac19Aa","doi-asserted-by":"crossref","unstructured":"Hale, J. (1977). Theory of Functional Differential Equations, Springer, New York, NY.","DOI":"10.1007\/978-1-4612-9892-2"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_020_w2aab3b7b4b1b6b1ab1ac20Aa","doi-asserted-by":"crossref","unstructured":"Joice Nirmala, R., Balachandran, K., Germa, L. and Trujillo, J. (2016). Controllability of nonlinear fractional delay dynamical systems, Reports on Mathematical Physics77(1): 87\u2013104.","DOI":"10.1016\/S0034-4877(16)30007-6"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_021_w2aab3b7b4b1b6b1ab1ac21Aa","unstructured":"Kaczorek, T. (2011). Selected Problems of Fractional Systems Theory, Springer, Berlin.10.1007\/978-3-642-20502-6"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_022_w2aab3b7b4b1b6b1ab1ac22Aa","unstructured":"Kilbas, A., Srivastava, H. and Trujillo, J. (2006). Theory and Application of Fractional Differential Equations, Elsevier, Amsterdam."},{"key":"2021040723004707401_j_amcs-2017-0035_ref_023_w2aab3b7b4b1b6b1ab1ac23Aa","doi-asserted-by":"crossref","unstructured":"Klamka, J. (1976a). Controllability of linear systems with time variable delay in control, International Journal of Control24(6): 869\u2013878.10.1080\/00207177608932867","DOI":"10.1080\/00207177608932867"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_024_w2aab3b7b4b1b6b1ab1ac24Aa","doi-asserted-by":"crossref","unstructured":"Klamka, J. (1976b). Relative controllability of nonlinear systems with delay in control, Automatica12(6): 633\u2013634.10.1016\/0005-1098(76)90046-7","DOI":"10.1016\/0005-1098(76)90046-7"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_025_w2aab3b7b4b1b6b1ab1ac25Aa","unstructured":"Klamka, J. (2000). Schauder\u2019s fixed-point theorem in nonlinear controllability problems, Control and Cybernetics29(1): 153\u2013165."},{"key":"2021040723004707401_j_amcs-2017-0035_ref_026_w2aab3b7b4b1b6b1ab1ac26Aa","doi-asserted-by":"crossref","unstructured":"Klamka, J. (2001). Constrained controllability of semilinear systems, Nonlinear Analysis47: 2939\u20132949.","DOI":"10.1016\/S0362-546X(01)00415-1"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_027_w2aab3b7b4b1b6b1ab1ac27Aa","unstructured":"Manzanilla, R., Marmol, L.G. and Vanegas, C.J. (2010). On the controllability of differential equation with delay, Abstract and Applied Analysis2010: 1\u201316, Article ID 307409.10.1155\/2010\/307409"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_028_w2aab3b7b4b1b6b1ab1ac28Aa","doi-asserted-by":"crossref","unstructured":"Morgado, M., Ford, N. and Lima, P. (2013). Analysis and numerical methods for fractional differential equation with delay, Journal of Computational and Applied Mathematics252: 159\u2013168.","DOI":"10.1016\/j.cam.2012.06.034"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_029_w2aab3b7b4b1b6b1ab1ac29Aa","unstructured":"Shamardan, A. and Moubarak, M. (1999). Controllability and observability for fractional control systems, Journal of Fractional Calculus15(1): 25\u201334."},{"key":"2021040723004707401_j_amcs-2017-0035_ref_030_w2aab3b7b4b1b6b1ab1ac30Aa","doi-asserted-by":"crossref","unstructured":"Wang, Z. (2013). A numerical method for delayed fractional order differential equations, Journal of Applied Mathematics2013: 1\u20137, Article ID 256071.","DOI":"10.1155\/2013\/256071"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_031_w2aab3b7b4b1b6b1ab1ac31Aa","doi-asserted-by":"crossref","unstructured":"Wiess, L. (1967). On the controllability of delayed differential systems, SIAM Journal of Control5(4): 575\u2013587.","DOI":"10.1137\/0305036"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_032_w2aab3b7b4b1b6b1ab1ac32Aa","unstructured":"Yi, S., Nelson, P.W. and Ulsoy, A.G. (2008). Controllability and observability of systems of linear delay differential equation via the matrix Lambert function, IEEE Transactions on Automatic Control53(3): 854\u2013860.10.1109\/TAC.2008.919549"},{"key":"2021040723004707401_j_amcs-2017-0035_ref_033_w2aab3b7b4b1b6b1ab1ac33Aa","doi-asserted-by":"crossref","unstructured":"Zhang, H., Cao, J. and Jiang, W. (2013). Controllability criteria for linear fractional differential systems with state delay impulse, Journal of Applied Mathematics2013: 1\u20139, Article ID 146010.","DOI":"10.1155\/2013\/146010"}],"container-title":["International Journal of Applied Mathematics and Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/amcs\/27\/3\/article-p501.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/amcs-2017-0035","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,15]],"date-time":"2024-05-15T22:57:27Z","timestamp":1715813847000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/amcs-2017-0035"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,1]]},"references-count":33,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,9,23]]},"published-print":{"date-parts":[[2017,9,1]]}},"alternative-id":["10.1515\/amcs-2017-0035"],"URL":"https:\/\/doi.org\/10.1515\/amcs-2017-0035","relation":{},"ISSN":["2083-8492"],"issn-type":[{"value":"2083-8492","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,1]]}}}