Effect of Climate Change and Fear in aFractional Prey-Predator Model withCrowley and Martin Functional Response

Effect of Climate Change and Fear in aFractional Prey-Predator Model withCrowley and Martin Functional Response | 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 Effect of Climate Change and Fear in aFractional Prey-Predator Model withCrowley and Martin Functional Response Chaimaa Assila, Hafida Benazza, Mohamed Reda Lemnouar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3999544/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract Global climate change is intensifying, with rising temperatures signifi-cantly impacting ecological relationships. Understanding the connectionbetween temperature and predation is imperative to address the threatof extinction resulting from excessive temperature increases. Inthispaper, we introduce a fractional prey-predator model incorporatingthe Caputo fractional operator. Our model considers prey-predatorinteractions based on Crowley and Martin’s functional response,account-ing for the fear effect induced by predation. We analyze the non-negativity, existence, uniqueness, and boundedness of solutions withinour model, considering both classical and Caputo derivative scenar-ios. Additionally, we investigate the local stability of each equilibriumunder both integer and fractional order conditions, emphasizing theglobal stability of the coexistence positive equilibrium point in bothcontexts. Our examination treats predation as a time-dependent func-tion, with the temperature function reflecting climate change andelucidating how rising temperatures contribute to predation. Throughnumerical simulations, we explore the impacts of fear on prey behav-ior and population dynamics, and illustrate how climate change,especially rising temperatures, intricately affects species relationships. Mathematics Subject Classification:26A33 , 34C60 , 34D20 , 92D25 , 37N25 Prey-predator model fractional-order Crowely and Martinfunctional response climate change fear effect Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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. 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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-3999544","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":278546421,"identity":"7e7adcd8-b21e-43fd-9730-e165c4929778","order_by":0,"name":"Chaimaa Assila","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBklEQVRIie2PsUoDQRRFb1jYSth2g+j+wgQrIcZfmWHBNBOwFAwkENgqxFbIN1gJU48O7DTitgOTIsEfWBBCQAjOCkFBxm0t5lSPxz28d4FA4D+SAvIwyzX6QCb96d8KxdXXplX5hkK1K8lytnk24wGSO72RdFyxh+W0U+8gMu+RVUkUL3OkhhNJS8vESkbdOWxv6lFISp0SR4A5cl1ip7hGx4Dt+JVhrfh+gqzSa0n3r40SfTjl0q9wokaFgvuKSFZIJgyNmyvMp7gK12q00Og1XdgiPxMvT8X5nNjcpyT3w8d3vr3FaaXf6no7OBF6pszuxl74lAOTH4GmOGnJBwKBQOBPPgEWRmXeeCQFPgAAAABJRU5ErkJggg==","orcid":"","institution":"University Moohammed V","correspondingAuthor":true,"prefix":"","firstName":"Chaimaa","middleName":"","lastName":"Assila","suffix":""},{"id":278546422,"identity":"a096a000-54d7-4557-9b97-5aabc37abf48","order_by":1,"name":"Hafida Benazza","email":"","orcid":"","institution":"University Moohammed V","correspondingAuthor":false,"prefix":"","firstName":"Hafida","middleName":"","lastName":"Benazza","suffix":""},{"id":278546423,"identity":"540f3bec-c990-4aa5-9777-0f383d6df87e","order_by":2,"name":"Mohamed Reda Lemnouar","email":"","orcid":"","institution":"University Moohammed V","correspondingAuthor":false,"prefix":"","firstName":"Mohamed","middleName":"Reda","lastName":"Lemnouar","suffix":""}],"badges":[],"createdAt":"2024-02-29 11:47:10","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-3999544/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-3999544/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":65946039,"identity":"850162a3-17c6-40f6-a5bc-d8469aab86fe","added_by":"auto","created_at":"2024-10-04 17:44:37","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2470348,"visible":true,"origin":"","legend":"","description":"","filename":"article.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3999544/v2_covered_22ca2b91-f034-46d3-b01f-5daf13e026b9.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eEffect of \u003cem\u003eClimate Change\u003c/em\u003e and Fear in aFractional Prey-Predator \u003cem\u003eModel\u003c/em\u003e withCrowley and Martin Functional Response\u003c/p\u003e","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":"Prey-predator model, fractional-order, Crowely and Martinfunctional response, climate change, fear effect","lastPublishedDoi":"10.21203/rs.3.rs-3999544/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3999544/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGlobal \u003cem\u003eclimate change\u003c/em\u003e is intensifying, with rising temperatures signifi-cantly impacting \u003cem\u003eecological\u003c/em\u003e relationships. Understanding the connectionbetween temperature and predation is imperative to address the threatof extinction resulting from excessive temperature increases. Inthispaper, we introduce a fractional prey-predator \u003cem\u003emodel\u003c/em\u003e incorporatingthe Caputo fractional operator. Our \u003cem\u003emodel\u003c/em\u003e considers prey-predatorinteractions based on Crowley and Martin’s functional response,account-ing for the fear effect induced by predation. We analyze the non-negativity, existence, uniqueness, and boundedness of solutions withinour \u003cem\u003emodel,\u003c/em\u003e considering both classical and Caputo derivative scenar-ios. Additionally, we investigate the \u003cem\u003elocal\u003c/em\u003e stability of each equilibriumunder both integer and fractional order conditions, emphasizing theglobal stability of the coexistence positive equilibrium point in bothcontexts. Our examination treats predation as a time-dependent func-tion, with the temperature function reflecting \u003cem\u003eclimate change\u003c/em\u003e andelucidating how rising temperatures contribute to predation. 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