{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T07:12:56Z","timestamp":1769152376593,"version":"3.49.0"},"reference-count":26,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,6,14]],"date-time":"2021-06-14T00:00:00Z","timestamp":1623628800000},"content-version":"vor","delay-in-days":164,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>This paper is presented on the theory and applications of the fractional\u2010order chaotic system described by the Caputo fractional derivative. Considering the new fractional model, it is important to establish the presence or absence of chaotic behaviors. The Lyapunov exponents in the fractional context will be our fundamental tool to arrive at our conclusions. The variations of the model\u2019s parameters will generate chaotic behavior, in general, which will be established using the Lyapunov exponents and bifurcation diagrams. For the system\u2019s phase portrait, we will present and apply an interesting fractional numerical discretization. For confirmation of the results provided in this paper, the circuit schematic is drawn and simulated. As it will be observed, the results obtained after the simulation of the numerical scheme and with the Multisim are in good agreement.<\/jats:p>","DOI":"10.1155\/2021\/5534872","type":"journal-article","created":{"date-parts":[[2021,6,15]],"date-time":"2021-06-15T00:05:08Z","timestamp":1623715508000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Study of a Fractional\u2010Order Chaotic System Represented by the Caputo Operator"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8664-6464","authenticated-orcid":false,"given":"Ndolane","family":"Sene","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,6,14]]},"reference":[{"key":"e_1_2_13_1_2","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/9845031"},{"key":"e_1_2_13_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2018.08.021"},{"key":"e_1_2_13_3_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218126619502396"},{"key":"e_1_2_13_4_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4977417"},{"key":"e_1_2_13_5_2","doi-asserted-by":"publisher","DOI":"10.3390\/e20050337"},{"key":"e_1_2_13_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2020.110200"},{"key":"e_1_2_13_7_2","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/8047347"},{"key":"e_1_2_13_8_2","doi-asserted-by":"publisher","DOI":"10.3390\/fractalfract4030035"},{"key":"e_1_2_13_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10470-018-1328-9"},{"key":"e_1_2_13_10_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207217.2018.1545260"},{"key":"e_1_2_13_11_2","doi-asserted-by":"publisher","DOI":"10.3390\/e20080564"},{"key":"e_1_2_13_12_2","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/1892618"},{"key":"e_1_2_13_13_2","doi-asserted-by":"publisher","DOI":"10.3390\/e20050384"},{"key":"e_1_2_13_14_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/i2019-12550-1"},{"key":"e_1_2_13_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.03.022"},{"key":"e_1_2_13_16_2","doi-asserted-by":"publisher","DOI":"10.1587\/elex.12.20141116"},{"key":"e_1_2_13_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2019.07.013"},{"key":"e_1_2_13_18_2","first-page":"1","article-title":"Design of an interface for random number generators based on integer and fractional order chaotic systems","volume":"1","author":"Akgul A.","year":"2019","journal-title":"Chaos Theory and Applications"},{"key":"e_1_2_13_19_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218126617501900"},{"key":"e_1_2_13_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-0208(06)80001-0"},{"key":"e_1_2_13_21_2","volume-title":"Fractional Differential Equations, Mathematics in Science and Engineering","author":"Podlubny I.","year":"1999"},{"key":"e_1_2_13_22_2","doi-asserted-by":"publisher","DOI":"10.22436\/jnsa.010.05.27"},{"key":"e_1_2_13_23_2","doi-asserted-by":"publisher","DOI":"10.3390\/math6020016"},{"key":"e_1_2_13_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2020.105413"},{"key":"e_1_2_13_25_2","doi-asserted-by":"crossref","unstructured":"BorahM. 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