Investigating Chaos in the Lorenz System based on Fractal-Fractional Derivatives

Investigating Chaos in the Lorenz System based on Fractal-Fractional Derivatives | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Investigating Chaos in the Lorenz System based on Fractal-Fractional Derivatives G. Alhamzi, Shivani Sharma, Dumitru Baleanu, Ravi Shanker Dubey This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8008674/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract \noindent The Lorenz system is known for its sensitivity to initial conditions, that is a little variation in the initial conditions gives drastically different trajectories over time. The Lorenz system is a classic example of deterministic chaos, wher random and complex behavior emerges from deterministic equations. This work focuses on the dynamical behaviour of the 5-Dimensional Mittag-Leffler-Fractal-Fractional order Lorenz system. The detailed proof for the existence of solution with uniqueness is given. The solutions are found numerically. Lastly, the dynamical behaviour are represented for distinct fractal-fractional order. 2020 Mathematics subject Classification. Primary 28A80, 65P20, 33E12; Secondary 26A33. Fractal-Fractional derivative Chaos Existence and Uniqueness Numerical Solutions Lorenz System Simulations Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 18 Feb, 2026 Reviews received at journal 18 Feb, 2026 Reviewers agreed at journal 10 Nov, 2025 Reviewers agreed at journal 05 Nov, 2025 Reviewers invited by journal 05 Nov, 2025 Editor assigned by journal 05 Nov, 2025 Submission checks completed at journal 05 Nov, 2025 First submitted to journal 01 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8008674","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":545657022,"identity":"49658b7a-d027-40bc-b743-2245510689dd","order_by":0,"name":"G. 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