Identifying an unknown coefficient in the fractional parabolic differential equation

Identifying an unknown coefficient in the fractional parabolic differential equation | 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 Identifying an unknown coefficient in the fractional parabolic differential equation Hamed Ould Sidi, M. J. Huntul, Maawiya Ould Sidi, Homan Emadifar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2386457/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 study, we considered a fractional parabolic equation for identifying the unknown diffusion coefficient from the noisy measurement of the ultimate time solution. It is an inverse problem involving a nonlocal operator that is nonlinear and poorly formulated. By demonstrating the existence of this inverse problem singular solution with regard to the final observed data, we demonstrate the identifiability of this problem. The inverse problem is expressed as a regularized optimization problem that minimizes a cost function of the least-squares kind. We have covered various theoretical and practical difficulties pertaining to the problem under consideration. It has been demonstrated that a unique stable solution to the optimization problem exists. The Morozov discrepancy principle and the conjugate gradient approach are used to develop an iterative reconstruction procedure. The accuracy and efficiency of the suggested method are illustrated using a few numerical examples. Fractional parabolic PDE Inverse potential problem Tikhonov’s regularization Conjugate gradient method Finit element methode Full Text Additional Declarations No competing interests reported. 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-2386457","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":162060716,"identity":"86f9115f-5e1a-4ed8-826a-262121866037","order_by":0,"name":"Hamed Ould Sidi","email":"","orcid":"","institution":"University of Nouakchott Al Aasriya","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Hamed","middleName":"Ould","lastName":"Sidi","suffix":""},{"id":162060717,"identity":"add1dacc-f3b1-44a2-a994-84f904aaf528","order_by":1,"name":"M. J. 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