Numerical analysis of a fractional-order giving up smoking model by using artificial neural network scheme

Numerical analysis of a fractional-order giving up smoking model by using artificial neural network scheme | 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 Article Numerical analysis of a fractional-order giving up smoking model by using artificial neural network scheme Muhammad Sadaqat Talha, Muhammad Waseem This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5232616/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 The aim of this study is to analyze the numerical performance of the fractional-order giving up smoking model (FO-GUSM) by developing a framework for computation by using stochastic Levenberg-Marquardt backpropagation artificial neural networks (SLMB-ANN). The GUSM is classif ied into four categories, potential smokers P(t), occasional smokers L(t), chain smoker S(t), and quit smoker Q(t). Computations are performed by SLMB-ANN to solve the four numerical variations. Using stochastic structured LMB-ANNs, the results obtained from GUSM were presented with training, validation, and testing processes to reduce the mean squared error (MSE) values compared to the reference (data-driven outcomes). To assess the efficiency, accuracy, capability, and proficiency of the suggested computational framework LMB-ANNs, a comprehensive analysis is conducted by analyzing correlations, mean square error (MSE), state transition data, error histograms, and regression analysis. The importance and value of the LMBANNs method is confirmed by the comparison of the results, achieving an accuracy within 5 to 7 decimal places in solving the GUSM. Physical sciences/Mathematics and computing/Applied mathematics Physical sciences/Mathematics and computing/Computational science Mathematical smoking model Diseased model Neural networks Numerical computing 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-5232616","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":377166879,"identity":"d7a85fcf-808a-4a24-bee4-b7b140775161","order_by":0,"name":"Muhammad Sadaqat Talha","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAElEQVRIiWNgGAWjYHACAwjFzsPA8KECyGBmbiBGi4EEAzMPA+OMMyAtjCRoYeZtAwkQ0CLffnjjhzc1f+r4m3kPfuCdVxvN3w7U8qNiG24rzqQVS845ZiAhcZgvWUJy2/HcGYcZGxh7ztzG46ocA2keNqDDDvMYSBhuO5bbANTCzNiGW4t8/xvj3zz/DCTkD/MY/0iccyx3PiEtDDdyzKR52wwkDA7zmEkcbKjJ3UBIi8GNZ2WWc/uMJTcCtVg2HDuQuxGo5SA+v8j3J2++8eabHL/c8R7j239q6nLnnT988MGPCjwOAwEeBPMwmDyAXz2qljqCikfBKBgFo2DkAQDrFlnycg7QlAAAAABJRU5ErkJggg==","orcid":"","institution":"COMSATS University Islamabad","correspondingAuthor":true,"prefix":"","firstName":"Muhammad","middleName":"Sadaqat","lastName":"Talha","suffix":""},{"id":377166880,"identity":"7f2e41b2-c2d8-4af9-97b9-18ab7d27ce48","order_by":1,"name":"Muhammad Waseem","email":"","orcid":"","institution":"COMSATS University Islamabad","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Waseem","suffix":""}],"badges":[],"createdAt":"2024-10-09 12:38:43","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-5232616/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5232616/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82035016,"identity":"06f47892-6149-44b0-9d78-5bbe8a670018","added_by":"auto","created_at":"2025-05-06 08:02:10","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3842581,"visible":true,"origin":"","legend":"","description":"","filename":"PaperLatex.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5232616/v1_covered_2a5e5b70-4b5d-42bf-87a8-13a76ce5927c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Numerical analysis of a fractional-order giving up smoking model by using artificial neural network scheme","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":"Mathematical smoking model, Diseased model, Neural networks, Numerical computing","lastPublishedDoi":"10.21203/rs.3.rs-5232616/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5232616/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The aim of this study is to analyze the numerical performance of the fractional-order giving up smoking model (FO-GUSM) by developing a framework for computation by using stochastic Levenberg-Marquardt backpropagation artificial neural networks (SLMB-ANN). 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