Existence and Hyers-Ulam stability results for abstract equations in Banach lattices and application

Existence and Hyers-Ulam stability results for abstract equations in Banach lattices and application | 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 Existence and Hyers-Ulam stability results for abstract equations in Banach lattices and application Nadir Benkaci-Ali This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1762530/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 are interested in the existence and Hyers-Ulam stability for the abstract equation in Banach lattices and application. In the application, we transform the given fractional differential system of (p₁,p₂,...,p n )-Laplacian Hilfer equations into an equivalent integral equation. Then we establish sufficient conditions and employ the fixed point index arguments and spectral theory to obtain new results on the existence and Hyers-Uulam stability. Examples illustrating the main theoritical results are also constructed. This work contains several new ideas, and gives a unified approach applicable to many types of initial value systems involving (p₁,p₂,...,p n )-Laplacian type operators 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. 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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-1762530","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":114206013,"identity":"0cb978ef-8d4d-4b2e-8aaf-bdfb7053c8df","order_by":0,"name":"Nadir Benkaci-Ali","email":"data:image/png;base64,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","orcid":"","institution":"University M'Hamed Bougara of Boumerdes","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Nadir","middleName":"","lastName":"Benkaci-Ali","suffix":""}],"badges":[],"createdAt":"2022-06-15 19:59:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1762530/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1762530/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":22959791,"identity":"2fd7cee0-ea5f-4751-9fe7-af7c306ad8b6","added_by":"auto","created_at":"2022-06-22 18:27:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":304415,"visible":true,"origin":"","legend":"","description":"","filename":"HUAb.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1762530/v1_covered.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Existence and Hyers-Ulam stability results for abstract equations in Banach lattices and application","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1762530/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":false,"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-1762530/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1762530/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we are interested in the existence and Hyers-Ulam stability for the abstract equation in Banach lattices and application. 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