Well-Posedness and Global Existence for Generalized Nonlinear Biharmonic Partial Differential Equations with Generalized Caputo Fractional Derivatives

Well-Posedness and Global Existence for Generalized Nonlinear Biharmonic Partial Differential Equations with Generalized Caputo Fractional Derivatives | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 27 January 2025 V1 Latest version Share on Well-Posedness and Global Existence for Generalized Nonlinear Biharmonic Partial Differential Equations with Generalized Caputo Fractional Derivatives Authors : Daoudi Aimen 0009-0008-0464-0984 , Abdelaziz Mennouni 0000-0002-0791-5866 [email protected] , and Mabrouk Meflah Authors Info & Affiliations https://doi.org/10.22541/au.173795432.25382432/v1 259 views 146 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This study analyzes the well-posedness and global existence of nonlinear biharmonic partial differential equations (PDEs) of the form ∂ t η, α w + w tt − γ 1 ∆ 2 w − γ 2 ∆ 2 w t + γ 3 w t + γ 4 w = γ 5 ∇ w g ( w ), involving the generalized Caputo fractional derivative of order 0 < α < 1 in time, where ( x, t ) ∈ Ω × R + . To validate our theoretical findings, we employ a finite difference approach for one-dimensional cases and use the Grünwald–Letnikov approximation. We also address the convergence of this numerical method. AMS Classification : 26A33, 34K37, 31A30, 49K40, 65N06 Supplementary Material File (paper 2v2.pdf) Download 4.52 MB Information & Authors Information Version history V1 Version 1 27 January 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords finite difference method fractional pdes generalized caputo fractional derivative global existence grünwald-letnikov approximation nonlinear biharmonic equations numerical convergence well-posedness Authors Affiliations Daoudi Aimen 0009-0008-0464-0984 Universite Kasdi Merbah Ouargla View all articles by this author Abdelaziz Mennouni 0000-0002-0791-5866 [email protected] Universite Batna 2 View all articles by this author Mabrouk Meflah Universite Kasdi Merbah Ouargla View all articles by this author Metrics & Citations Metrics Article Usage 259 views 146 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Daoudi Aimen, Abdelaziz Mennouni, Mabrouk Meflah. Well-Posedness and Global Existence for Generalized Nonlinear Biharmonic Partial Differential Equations with Generalized Caputo Fractional Derivatives. Authorea . 27 January 2025. DOI: https://doi.org/10.22541/au.173795432.25382432/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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