Backstepping sliding mode control for coupled delayed time fractional reaction diffusion systems subject to boundary input disturbances

Backstepping sliding mode control for coupled delayed time fractional reaction diffusion systems subject to boundary input disturbances | 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 Backstepping sliding mode control for coupled delayed time fractional reaction diffusion systems subject to boundary input disturbances Juan Chen, Bo Zhuang, YangQuan Chen, Yajuan Yu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-438964/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this paper we develop backstepping-based boundary sliding mode controllers for coupled time fractional reaction diffusion (FRD) systems governed by time fractional partial differential equations (PDEs) with time varying delay and input disturbances. Here, the diffusion coefficients are spatially varying (nonconstant) and can be same or different. To asymptotically stabilize the system, we first use a backstepping transformation to convert the original dynamics into a target dynamics with a new manipulable input and the perturbation. Then, the sliding mode algorithm is employed to design this discontinuous controller to suppress disturbances. In this case, we obtain the combined backstepping/sliding mode controller of the original dynamics, with which the closed-loop asymptotic stability is proved by the fractional Halanay's inequality. Fractional numerical examples are given to demonstrate the efficiency of the proposed synthesis. Computational Mathematics Coupled time fractional reaction diffusion systems Time varying delay Boundary sliding mode control Input disturbances Backstepping Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Full Text Cite Share Download PDF Status: Posted Version 1 posted 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-438964","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":22117408,"identity":"51afe9a9-31ad-40e5-98e4-a89ff66dd895","order_by":0,"name":"Juan Chen","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-9384-9059","institution":"Changzhou University - 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