Local Fractional Sturm-Liouville Theory on Fractal Sets with Integration by Parts and Equivalence of Local Fractional Derivatives

Local Fractional Sturm-Liouville Theory on Fractal Sets with Integration by Parts and Equivalence of Local Fractional Derivatives | 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 Local Fractional Sturm-Liouville Theory on Fractal Sets with Integration by Parts and Equivalence of Local Fractional Derivatives Taylan Demir, Niaz Ali Shah This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8960159/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 An approach to creating a fractional version of the Sturm and Liouville theorem for an inter val by means of integration by parts as a structural axiom will be described. The relationship between some properties and definitions of this development will be proven formally as having equivalents under appropriate admissibility conditions; creating an adjointly unique structure. This theory leads to developing self adjoint local fractional Sturm and Liouville operators with orthogonal eigenfunctions having real spectra. The stair step variable is provided as an explicit example of the creation of a spectral structure on fractals. 2020 Mathematics Subject Classification. Primary 34L10; Secondary 26A33, 28A80, 47A75. Applied Mathematics Analysis Local fractional calculus Fractal sets Staircase function Integration by parts Equivalence of fractional derivatives Sturm–Liouville operators Self-adjointness Spectral theory on fractals Full Text Additional Declarations The authors declare no competing interests. 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. 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The relationship between some properties and definitions of this development will be proven formally as having equivalents under appropriate admissibility conditions; creating an adjointly unique structure. This theory leads to developing self adjoint local fractional Sturm and Liouville operators with orthogonal eigenfunctions having real spectra. The stair step variable is provided as an explicit example of the creation of a spectral structure on fractals.\u003c/p\u003e\n\u003cp\u003e2020 Mathematics Subject Classification. 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