Fractional Stochastic Dynamics and Stability Analysis of Drone Swarms in Random Urban Environments

Fractional Stochastic Dynamics and Stability Analysis of Drone Swarms in Random Urban Environments | 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 Fractional Stochastic Dynamics and Stability Analysis of Drone Swarms in Random Urban Environments Mohamed-Ahmed BOUDREF This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9420195/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 work develops a mathematical model that describes the collective motion of drone swarms evolving in uncertain urban environments. The dynamics combine fractional stochastic differential equations with Markov switching interaction graphs and an environmental velocity field governed by a stochastic partial differential equation, allowing the simultaneous incorporation of memory effects, stochastic perturbations, and spatial correlations. The existence and uniqueness of solutions are established under standard Lipschitz and growth conditions. A Lyapunov approach adapted to fractional dynamics yields mean-square stability results expressed in terms of Mittag-Leffler decay. A spectral analysis of the interaction structure is also provided, showing how convergence properties are governed by the eigenvalues of the Laplacian together with the fractional order. The results characterize cooperative behavior of the swarm under memory effects, switching topologies, and spatially correlated disturbances. MSC (2020): 34A08, 60H15, 60J60, 93C15, 93D20. Fractional stochastic systems drone swarms consensus dynamics stochastic partial differential equations Markov switching Lyapunov stability spectral analysis 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-9420195","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":624265329,"identity":"1c39bb92-5a45-4666-931d-00888e9ab62c","order_by":0,"name":"Mohamed-Ahmed BOUDREF","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA70lEQVRIiWNgGAWjYFACHiBmY2Bgb29gYEgAI0Ygi4GZsBaeMwdI1nIjAcxNgArj1qLbwHvwMU/ZPTkeyTdmDx62MeTxSyS3ffjBYG2PS4vZAb5kY55zxcY80jnmBoltDMWSMxKbZ/YwpOO0xuwAj5k0b1tC4n7pHDOJhDP/EzfcSGwGuvYwGyEt9T2SZ0BaGMBaGP8wHOYhpCWBR4IHqKUCooUZaIsETi2H+ZIN55xLMOzhSSsDaSmW7HnYzCxjkG6AU8vx3oMP3pQlyPOwH94m+cMAGGLs6Y8Z31TgDjFc4Y/TjlEwCkbBKBgFxAAAD3BMATgHmnEAAAAASUVORK5CYII=","orcid":"","institution":"University of Bouira","correspondingAuthor":true,"prefix":"","firstName":"Mohamed-Ahmed","middleName":"","lastName":"BOUDREF","suffix":""}],"badges":[],"createdAt":"2026-04-15 00:53:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9420195/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9420195/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108805295,"identity":"e9b1020c-76f4-48ec-a8b7-a6eaea8fb091","added_by":"auto","created_at":"2026-05-08 15:25:30","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":214647,"visible":true,"origin":"","legend":"","description":"","filename":"FractionalStochasticDynamicsandStabilityAnalysisofDroneSwarmsinRandomUrbanEnvironments.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9420195/v1_covered_0bb4c36f-f0b7-4bfe-a2ea-9edac0e287ec.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Fractional Stochastic Dynamics and Stability Analysis of Drone Swarms in Random Urban Environments","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":"Fractional stochastic systems, drone swarms, consensus dynamics, stochastic partial differential equations, Markov switching, Lyapunov stability, spectral analysis","lastPublishedDoi":"10.21203/rs.3.rs-9420195/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9420195/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis work develops a mathematical model that describes the collective motion of drone swarms evolving in uncertain urban environments. The dynamics combine fractional stochastic differential equations with Markov switching interaction graphs and an environmental velocity field governed by a stochastic partial differential equation, allowing the simultaneous incorporation of memory effects, stochastic perturbations, and spatial correlations.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe existence and uniqueness of solutions are established under standard Lipschitz and growth conditions. A Lyapunov approach adapted to fractional dynamics yields mean-square stability results expressed in terms of Mittag-Leffler decay.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eA spectral analysis of the interaction structure is also provided, showing how convergence properties are governed by the eigenvalues of the Laplacian together with the fractional order.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe results characterize cooperative behavior of the swarm under memory effects, switching topologies, and spatially correlated disturbances.\u003c/p\u003e\n\u003cp\u003eMSC (2020): 34A08, 60H15, 60J60, 93C15, 93D20.\u003c/p\u003e","manuscriptTitle":"Fractional Stochastic Dynamics and Stability Analysis of Drone Swarms in Random Urban Environments","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-27 13:20:51","doi":"10.21203/rs.3.rs-9420195/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"10552815-c523-4c1a-88bc-70ff47f7e1d2","owner":[],"postedDate":"April 27th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Rejected","date":"2026-05-07T06:03:25+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-05-07T06:11:18+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-27 13:20:51","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9420195","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9420195","identity":"rs-9420195","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}