Numerical solution of nonlinear multi-term weakly singular fractional Volterra integro-differential equations using Jacobi collocation method

Numerical solution of nonlinear multi-term weakly singular fractional Volterra integro-differential equations using Jacobi collocation method | 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 Numerical solution of nonlinear multi-term weakly singular fractional Volterra integro-differential equations using Jacobi collocation method Qasim Hadi Haddam, Esmaeil Najafi, Saeed Sohabi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4186485/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 paper deals with the numerical solution of a class of nonlinear multi-term weakly singular fractional Volterra integro-differential equations by ‎Jacobi ‎collocation method based on the orthogonal polynomials‎. ‎Since the solution of the proposed equation is not smooth enought ‎in the origin‎, thus t‎he ‎idea ‎of ‎the ‎smoothing ‎transformation ‎is ‎used ‎on the equation ‎‎to ‎incearse ‎the ‎smoothness ‎of ‎the ‎solution. ‎‎We ‎represent‎ an operator-based ‎discus‎sion ‎of ‎smoothing ‎transformation ‎an‎d Gauss-Jacobi ‎quadrature‎ ‎for ‎Riemann-‎Liou‎ville ‎integral ‎operators‎ ‎and ‎weakly ‎singular ‎integral ‎operators ‎using ‎their ‎similar ‎constructions‎ ‎and ‎extend ‎it ‎to ‎the ‎error ‎analysis ‎of ‎the ‎proposed ‎method ‎and ‎obtain ‎an ‎error ‎bound ‎for ‎the ‎discrete ‎collocation ‎solution. ‎To ‎test ‎the ‎efficiency ‎and ‎accuracy, ‎‎‎various ‎numerical ‎examples ‎are ‎solved ‎by‎ the ‎pr‎oposed ‎method and the ‎obtained‎ ‎error‎ results are in accordance with the ‎convergence ‎analysis ‎of ‎the ‎method.‎‎‎‎‎‎ 2020 MSC: 26A33, 65R20, 65M70 Fractional calculus multi-term Volterra integro-differential equations Jacobi collocation method Smoothing transformation 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-4186485","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":288905131,"identity":"0633bc97-9013-4453-83b3-32b528856fa9","order_by":0,"name":"Qasim Hadi Haddam","email":"","orcid":"","institution":"Urmia University","correspondingAuthor":false,"prefix":"","firstName":"Qasim","middleName":"Hadi","lastName":"Haddam","suffix":""},{"id":288905132,"identity":"7c130d98-3240-425f-a048-8aa35923f33d","order_by":1,"name":"Esmaeil 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Smoothing transformation","lastPublishedDoi":"10.21203/rs.3.rs-4186485/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4186485/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e‎This paper deals with the numerical solution of a class of nonlinear multi-term weakly singular fractional Volterra integro-differential equations by ‎Jacobi ‎collocation method based on the orthogonal polynomials‎. ‎Since the solution of the proposed equation is not smooth enought ‎in the origin‎, thus t‎he ‎idea ‎of ‎the ‎smoothing ‎transformation ‎is ‎used ‎on the equation ‎‎to ‎incearse ‎the ‎smoothness ‎of ‎the ‎solution. ‎‎We ‎represent‎ an operator-based ‎discus‎sion ‎of ‎smoothing ‎transformation ‎an‎d Gauss-Jacobi ‎quadrature‎ ‎for ‎Riemann-‎Liou‎ville ‎integral ‎operators‎ ‎and ‎weakly ‎singular ‎integral ‎operators ‎using ‎their ‎similar ‎constructions‎ ‎and ‎extend ‎it ‎to ‎the ‎error ‎analysis ‎of ‎the ‎proposed ‎method ‎and ‎obtain ‎an ‎error ‎bound ‎for ‎the ‎discrete ‎collocation ‎solution. ‎To ‎test ‎the ‎efficiency ‎and ‎accuracy, ‎‎‎various ‎numerical ‎examples ‎are ‎solved ‎by‎ the ‎pr‎oposed ‎method and the ‎obtained‎ ‎error‎ results are in accordance with the ‎convergence ‎analysis ‎of ‎the ‎method.‎‎‎‎‎‎\u003c/p\u003e\n\u003cp\u003e2020 MSC: 26A33, 65R20, 65M70\u003c/p\u003e","manuscriptTitle":"Numerical solution of nonlinear multi-term weakly singular fractional Volterra integro-differential equations using Jacobi collocation method","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-11 18:25:18","doi":"10.21203/rs.3.rs-4186485/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research 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