On the fractional relaxation equation with Scarpi derivative

On the fractional relaxation equation with Scarpi derivative | 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 Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed.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. 15 October 2025 V1 Latest version Share on On the fractional relaxation equation with Scarpi derivative Authors : Matija Adam Horvat and Nikola Sarajlija 0000-0003-2055-998X [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176051919.99747926/v1 165 views 108 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In this article we solve the Cauchy problem for the relaxation equation posed in a framework of variable order fractional calculus. After introducing some general mathematical theory we establish concepts of Scarpi derivative and transition functions which represent the essentials of our problem. Next, we provide an expression in terms of an integral for the solution of our initial value problem where the transition function is chosen arbitrary. Finally, we provide the special case of the integral for the solution in the case of an exponential-type transition function, as well as in the case of a Mittag-Leffler transition. Supplementary Material File (mmas_manuscript_final.pdf) Download 387.00 KB Information & Authors Information Version history V1 Version 1 15 October 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords fractional calculus relaxation equation scarpi derivative Authors Affiliations Matija Adam Horvat Univerzitet u Novom Sadu View all articles by this author Nikola Sarajlija 0000-0003-2055-998X [email protected] Univerzitet u Novom Sadu View all articles by this author Metrics & Citations Metrics Article Usage 165 views 108 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Matija Adam Horvat, Nikola Sarajlija. On the fractional relaxation equation with Scarpi derivative. Authorea . 15 October 2025. DOI: https://doi.org/10.22541/au.176051919.99747926/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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