Hybrid Spectral-Adomian Method for Nonlinear Stochastic Fractional Integro-Differential Equations on Time Scales

Hybrid Spectral-Adomian Method for Nonlinear Stochastic Fractional Integro-Differential Equations on Time Scales | 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 Hybrid Spectral-Adomian Method for Nonlinear Stochastic Fractional Integro-Differential Equations on Time Scales RACHID LIBOURKI, TJANG DANIEL CHANDRA This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6768620/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 study explored the challenges of solving nonlinear stochastic fractional integro-differential equations on time scales, which are critical in various applied mathematics and engineering problems. The complexity of these equations and the lack of efficient analytical methods highlighted the need for an improved computational approach.The aim of the research was to develop a hybrid spectral-Adomian decomposition method to solve these types of equations with enhanced accuracy and efficiency. The focus was on bridging existing methodological gaps and providing a robust tool for researchers dealing with stochastic fractional systems. The method involved integrating the spectral method with the Adomian decomposition technique to create a hybrid algorithm. Numerical experiments were carried out on benchmark problems to assess the performance of the proposed method, and computational tests were implemented using MATLAB.The results indicated that the hybrid spectral-Adomian method achieved superior accuracy and faster convergence compared to conventional methods. The numerical solutions closely matched exact results where available, confirming the method’s validity and reliability.The study concluded that the hybrid method is a highly effective approach for solving nonlinear stochastic fractional integro-differential equations on time scales. It demonstrated significant improvements over traditional numerical schemes, making it a valuable addition to computational mathematics.This research contributed a new hybrid numerical method that combines the strengths of spectral accuracy with the flexibility of the Adomian decomposition method. The findings are expected to benefit the field of applied mathematics, particularly in advancing solution techniques for complex stochastic systems, aligning with the journal’s scope. Adomian decomposition fractional differential equations spectral method stochastic systems time-scale calculus integro-differential equations 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-6768620","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":468160788,"identity":"743e002a-5bbd-49e2-9ab3-5a3fcbb62b30","order_by":0,"name":"RACHID LIBOURKI","email":"data:image/png;base64,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","orcid":"","institution":"State University of Malang","correspondingAuthor":true,"prefix":"","firstName":"RACHID","middleName":"","lastName":"LIBOURKI","suffix":""},{"id":468160789,"identity":"ed90712f-dd14-4cdc-8737-ac7a99b15793","order_by":1,"name":"TJANG DANIEL CHANDRA","email":"","orcid":"","institution":"State University of Malang","correspondingAuthor":false,"prefix":"","firstName":"TJANG","middleName":"DANIEL","lastName":"CHANDRA","suffix":""}],"badges":[],"createdAt":"2025-05-28 13:38:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6768620/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6768620/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84284330,"identity":"1f996fed-951a-4c4b-beae-a5c5f6113a7d","added_by":"auto","created_at":"2025-06-10 07:23:02","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":380079,"visible":true,"origin":"","legend":"","description":"","filename":"HybridSpectralAdomianMethodforNonlinearStochasticFractionalIntegroDifferentialEquationsonTimeScales.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6768620/v1_covered_fdc602b0-5251-41bd-81f6-0790bc2c0d37.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Hybrid Spectral-Adomian Method for Nonlinear Stochastic Fractional Integro-Differential Equations on Time Scales","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Adomian decomposition fractional differential equations; spectral method; stochastic systems; time-scale calculus; integro-differential equations","lastPublishedDoi":"10.21203/rs.3.rs-6768620/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6768620/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study explored the challenges of solving nonlinear stochastic fractional integro-differential equations on time scales, which are critical in various applied mathematics and engineering problems. 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