Analysis of Solutions of Fuzzy Differential Equations under the Generalized Derivative

Analysis of Solutions of Fuzzy Differential Equations under the Generalized Derivative | 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 Analysis of Solutions of Fuzzy Differential Equations under the Generalized Derivative Felipe Longo, Beatriz Laiate, Marta Cilene Gadotti, João Frederico da Costa Azevedo Meyer This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5195079/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 Feb, 2026 Read the published version in Soft Computing → Version 1 posted 5 You are reading this latest preprint version Abstract This work investigates the existence of non-gH \(\ast\) -solutions of fuzzy differential equations under g-derivative. We begin by establishing a theorem that extend the calculus fundamental theorem to the fuzzy context of g-differentiability. After some particular examples that help understand the possible cases for such differential equations, some results are settled giving the necessary conditions for each one of the observed behaviors and more. fuzzy differential equation fuzzy derivatives fuzzy integrals Full Text Cite Share Download PDF Status: Published Journal Publication published 11 Feb, 2026 Read the published version in Soft Computing → Version 1 posted Editor assigned by journal 10 Mar, 2025 Reviewers agreed at journal 12 Nov, 2024 Reviewers invited by journal 12 Nov, 2024 Editor invited by journal 06 Nov, 2024 First submitted to journal 02 Oct, 2024 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. 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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-5195079","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":377050576,"identity":"4e4a7083-6a38-4d35-a3b5-949b6852f392","order_by":0,"name":"Felipe Longo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA00lEQVRIiWNgGAWjYBACPjBZIQHhJYBJHvxa2MDkGZK1MLahiBHSwt57+MXHeRbR/Aw8Zg8e1NhFmzPwHvuAVwvPuTTLmdskcmc28JgbJBxLzt3ZwJc8A68WiRwzY16glg0HeMwkEhuYQQxj/A4Da5kjkbsfoqWeKC3Gj3kbgLYwgLUcJkILzxkzxhnHJHJnHGYrk0g4djx3ZzNfMl4t/Ow9xh8+1NTl9rc3b5P8UVOdux0Yhni1gN0GppihXANm3EphgBk1FgwI6xgFo2AUjIIRBgA9vkDib0U1kgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-2868-3937","institution":"UNICAMP: Universidade Estadual de Campinas","correspondingAuthor":true,"prefix":"","firstName":"Felipe","middleName":"","lastName":"Longo","suffix":""},{"id":377050577,"identity":"7865228a-4a5d-457c-9803-c626ee27ae6c","order_by":1,"name":"Beatriz Laiate","email":"","orcid":"","institution":"FGV: Fundacao Getulio Vargas","correspondingAuthor":false,"prefix":"","firstName":"Beatriz","middleName":"","lastName":"Laiate","suffix":""},{"id":377050578,"identity":"af1606cb-7a30-4fc2-bcf5-12f9f72e747d","order_by":2,"name":"Marta Cilene Gadotti","email":"","orcid":"","institution":"UNESP IGCERC: Universidade Estadual Paulista Julio de Mesquita Filho Instituto de Geociencias e Ciencias Exatas","correspondingAuthor":false,"prefix":"","firstName":"Marta","middleName":"Cilene","lastName":"Gadotti","suffix":""},{"id":377050579,"identity":"0ba40a4f-2106-4e45-8d72-5f6f03f65626","order_by":3,"name":"João Frederico da Costa Azevedo Meyer","email":"","orcid":"","institution":"UNICAMP: Universidade Estadual de Campinas","correspondingAuthor":false,"prefix":"","firstName":"João","middleName":"Frederico da Costa Azevedo","lastName":"Meyer","suffix":""}],"badges":[],"createdAt":"2024-10-02 22:41:44","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5195079/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5195079/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00500-026-11183-4","type":"published","date":"2026-02-11T15:57:12+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":102785169,"identity":"09bac25b-8dbe-467c-90a6-d245d40c7327","added_by":"auto","created_at":"2026-02-16 16:00:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":609113,"visible":true,"origin":"","legend":"","description":"","filename":"SOCOD2404421reviewer.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5195079/v1_covered_42cb62d9-a840-4c2f-97c8-0dbe8fc2fc7a.pdf"}],"financialInterests":"","formattedTitle":"Analysis of Solutions of Fuzzy Differential Equations under the Generalized Derivative","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"soft-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"soco","sideBox":"Learn more about [Soft Computing](https://www.springer.com/journal/500)","snPcode":"500","submissionUrl":"https://submission.nature.com/new-submission/500/3","title":"Soft Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"fuzzy differential equation, fuzzy derivatives, fuzzy integrals","lastPublishedDoi":"10.21203/rs.3.rs-5195079/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5195079/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis work investigates the existence of non-gH\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ast\\)\u003c/span\u003e\u003c/span\u003e-solutions of fuzzy differential equations under g-derivative. 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