{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T15:52:51Z","timestamp":1765295571597,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T00:00:00Z","timestamp":1744761600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Fractional calculus generalizes well-known differentiation and integration to noninteger orders, allowing a more accurate framework for modeling complex dynamical behaviors. The application of fractional-order systems is quite wide in engineering, biology, and physics because they inherently capture the memory effects and long-range dependencies. Out of these, fractional jerk chaotic systems have gained attention regarding their applications in secure communication, signal processing, and control systems. This work develops a comparative analysis of a fractional jerk system that includes constant- and variable-order derivatives to contribute to chaos\u2013stability analysis. Additionally, this study uncovers novel chaotic behaviors, further expanding our understanding of complex dynamical systems. The results yield new insights into using variable-order dynamics to enable chaotic systems to better adapt to real applications.<\/jats:p>","DOI":"10.3390\/sym17040605","type":"journal-article","created":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T10:04:56Z","timestamp":1744797896000},"page":"605","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Exploring Chaos in Fractional Order Systems: A Study of Constant and Variable-Order Dynamics"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6472-6589","authenticated-orcid":false,"given":"Reem","family":"Allogmany","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah P.O. Box 344, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7714-0173","authenticated-orcid":false,"given":"Nada A.","family":"Almuallem","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2150-8228","authenticated-orcid":false,"given":"Reima Daher","family":"Alsemiry","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, College of Science, Taibah University, Yanbu 41911, Al-Madinah Al-Munawarah, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0509-1506","authenticated-orcid":false,"given":"Mohamed A.","family":"Abdoon","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, Common First Year Deanship, King Saud University, P.O. Box 1142, Riyadh 12373, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,16]]},"reference":[{"key":"ref_1","first-page":"1021","article-title":"Applications of fractional calculus","volume":"4","author":"Dalir","year":"2010","journal-title":"Appl. Math. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.cnsns.2018.04.019","article-title":"A new collection of real world applications of fractional calculus in science and engineering","volume":"64","author":"Sun","year":"2018","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"639801","DOI":"10.1155\/2010\/639801","article-title":"Some applications of fractional calculus in engineering","volume":"2010","author":"Machado","year":"2010","journal-title":"Math. Probl. 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