A Novel Laplace-Based Decomposition Technique for Fractional Navier–Stokes Systems with Memory Effects

A Novel Laplace-Based Decomposition Technique for Fractional Navier–Stokes Systems with Memory Effects | 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 Novel Laplace-Based Decomposition Technique for Fractional Navier–Stokes Systems with Memory Effects Tariq A. Alarareh, Amirah Azmi, Hamzeh Taha Alkasasbeh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7666607/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 12 You are reading this latest preprint version Abstract This study presents a novel enhancement to the classical Laplace Transform Adomian Decomposition Method (LT-ADM) for the numerical solution of two-dimensional time-fractional Navier--Stokes equations involving the Atangana--Baleanu--Caputo (ABC) derivative. The proposed Modified LT-ADM (MLT-ADM) integrates an optimized, problem-adapted initial approximation obtained via a least-squares residual minimization framework. This modification enables the method to achieve high-accuracy solutions with a single iteration, markedly reducing computational overhead compared to its classical counterpart. Analytical investigations on and stability confirm the theoretical soundness of the proposed formulation, particularly in regimes dominated by strong memory and nonlocal effects. Numerical results further demonstrate the method’s capacity to deliver error reductions of several orders of magnitude while preserving physical fidelity across a wide spectrum of fractional orders. The synergy between the non-singular ABC operator and the optimized decomposition structure positions MLT-ADM as a robust, accurate, and scalable tool for simulating complex fractional fluid dynamics, with promising extensibility to higher-dimensional, variable-order, and coupled multiphysics systems. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Fractional Navier–Stokes equations Laplace Transform Adomian Decomposition Method Atangana–Baleanu–Caputo derivative optimized initial approximation semi-analytical methods fluid dynamics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 11 Nov, 2025 Reviews received at journal 30 Oct, 2025 Reviews received at journal 19 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers agreed at journal 09 Oct, 2025 Reviewers agreed at journal 09 Oct, 2025 Reviewers agreed at journal 09 Oct, 2025 Reviewers invited by journal 09 Oct, 2025 Editor assigned by journal 09 Oct, 2025 Editor invited by journal 07 Oct, 2025 Submission checks completed at journal 03 Oct, 2025 First submitted to journal 03 Oct, 2025 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-7666607","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":531871323,"identity":"f2c2ce38-1c4d-49bf-a27e-d2fc020490e1","order_by":0,"name":"Tariq A. 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