Decoupled matrix Riccati differential equations approach for robust boundary data completion in time-fractional diffusion problems

Decoupled matrix Riccati differential equations approach for robust boundary data completion in time-fractional diffusion problems | 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 Decoupled matrix Riccati differential equations approach for robust boundary data completion in time-fractional diffusion problems Fadhel Jday, Ridha Mdimagh, Haithem Omri This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3645615/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 This research introduces an innovative algorithmic framework tailored to solve the inverse boundary data completion problem for time-fractional diffusion equations in a bounded domain, especially under partially specified Neumann and Dirichlet conditions. This issue is notoriously ill-posed in the Hadamard sense which demands a sophisticated and nuanced approach. Our method innovatively transforms this problem into a system of first-order differential equations, linked with Matrix Riccati Differential Equations. Moving beyond traditional methods, our framework integrates a state-of-the-art decoupling algorithm, which effectively blends the strategic depth of optimal control theory with the precision of the Golden Section Search algorithm. This integration determines the optimal regularization parameter essential for ensuring the stability and the reliability of the solution. The robustness and effectiveness of our approach have been rigorously verified through extensive numerical experiments, proving its resilience even in conditions marked by significant noise levels. AMS Subject Classifications: 34K20, 35Pxx, 35S16, 60K50, 35R11 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-3645615","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":252081551,"identity":"19c076fd-9a81-44b6-acdc-000429a2de52","order_by":0,"name":"Fadhel Jday","email":"","orcid":"","institution":"Umm al-Qura University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Fadhel","middleName":"","lastName":"Jday","suffix":""},{"id":252081552,"identity":"25a9b5be-5ce9-43dc-8a33-dbf7d10039fa","order_by":1,"name":"Ridha Mdimagh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVRIiWNgGAWjYJACZhDBxt7AYABlEwSMzSCSj+cAqVrkJBLgNuIH5tMOH39cmGOXxyb5xqCAocI6sYH/8AO8WmRupyU2z9yWXMwmnWNgwHAmPbFBIs0ArxYJ6RzDZt5tzIltIC2MbYeBWhiI0lKf2CZ5BqjlH1AL//EPxGg5nNgmwQPU0gDUwpBDyJa0xNm8244ntvGkFRgkHEs3bpPIKSCgJfnAZ95t1Ynz2w9vM/hQYy3bz398A14tyIDNIAFEEq0eCJgfkKJ6FIyCUTAKRg4AAFCiQCXaCV76AAAAAElFTkSuQmCC","orcid":"","institution":"Jeddah University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Ridha","middleName":"","lastName":"Mdimagh","suffix":""},{"id":252081553,"identity":"6639521d-7e3b-45ee-857a-10049210e536","order_by":2,"name":"Haithem Omri","email":"","orcid":"","institution":"National Engineering School of Tunis","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Haithem","middleName":"","lastName":"Omri","suffix":""}],"badges":[],"createdAt":"2023-11-21 20:29:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3645615/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3645615/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":48479753,"identity":"4b85b02d-5345-4d7a-9a9a-03a39a31eea3","added_by":"auto","created_at":"2023-12-19 18:07:48","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":710046,"visible":true,"origin":"","legend":"","description":"","filename":"Fractionaldiffusionequation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3645615/v1_covered_75bfd784-98a2-4d50-b09c-970de959bf1d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Decoupled matrix Riccati differential equations approach for robust boundary data completion in time-fractional diffusion problems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3645615/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3645615/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis research introduces an innovative algorithmic framework tailored to solve the inverse boundary data completion problem for time-fractional diffusion equations in a bounded domain, especially under partially specified Neumann and Dirichlet conditions. 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