A robust multi-step predictor-corrector method for solving fractional order biological models

A robust multi-step predictor-corrector method for solving fractional order biological models | 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 A robust multi-step predictor-corrector method for solving fractional order biological models D. Elago, S. M. Nuugulu, K. C. Patidar, F. Gideon This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8987823/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 10 You are reading this latest preprint version Abstract This paper develops a new multi-step predictorcorrector numerical scheme for the approximate solution of fractional-order biological models with Caputo derivatives of order 0 < α ≤ 1. The proposed method extends the classical Adams-Bashforth-Moulton framework to the fractional setting by replacing the standard Lagrange polynomial interpolation with binomial coecients derived from Euler's gamma function. A three-step fractional Adams-Bashforth predictor is coupled with a two-step fractional Adams-Moulton corrector to form a unied scheme. Existence and uniqueness of solutions are established using xed-point arguments, while consistency, stability, and convergence of the numerical method are rigorously analysed. It is shown that the combined scheme is stable and convergent with order O(h 2α). Truncation and global error bounds are derived, and convergence rates are veried numerically using the double mesh principle. The performance of the method is assessed on three representative fractional-order biological models, including ecological predator-prey dynamics and epidemiological SIR and SEIR systems. Numerical experiments demonstrate that the scheme is robust, accurate, and well suited for nonlinear models exhibiting memory eects. The results further indicate that smaller fractional orders are particularly eective in capturing fast epidemic dynamics, while larger orders are more appropriate for ecological systems with longer memory. Physical sciences/Mathematics and computing Physical sciences/Physics Fractional Calculus Fractional Order Biological Model Adams-Bashforth-Moulton Predictor-Corrector Method Stability Analysis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 27 Apr, 2026 Reviews received at journal 18 Apr, 2026 Reviews received at journal 18 Apr, 2026 Reviewers agreed at journal 30 Mar, 2026 Reviewers agreed at journal 30 Mar, 2026 Reviewers invited by journal 30 Mar, 2026 Editor invited by journal 29 Mar, 2026 Editor assigned by journal 06 Mar, 2026 Submission checks completed at journal 06 Mar, 2026 First submitted to journal 27 Feb, 2026 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-8987823","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":614696457,"identity":"ccdd86f0-6de0-4071-b1e9-60bc9bc86691","order_by":0,"name":"D. 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The proposed method extends the classical Adams-Bashforth-Moulton framework to the fractional setting by replacing the standard Lagrange polynomial interpolation with binomial coecients derived from Euler's gamma function. A three-step fractional Adams-Bashforth predictor is coupled with a two-step fractional Adams-Moulton corrector to form a unied scheme. Existence and uniqueness of solutions are established using xed-point arguments, while consistency, stability, and convergence of the numerical method are rigorously analysed. It is shown that the combined scheme is stable and convergent with order O(h 2α). Truncation and global error bounds are derived, and convergence rates are veried numerically using the double mesh principle. The performance of the method is assessed on three representative fractional-order biological models, including ecological predator-prey dynamics and epidemiological SIR and SEIR systems. 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