{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T16:10:43Z","timestamp":1773677443069,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,12]],"date-time":"2024-09-12T00:00:00Z","timestamp":1726099200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Eastern Mediterranean University","award":["BABC-04-23-01"],"award-info":[{"award-number":["BABC-04-23-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this research paper, we consider a model of the fractional Cauchy\u2013Euler-type equation, where the fractional derivative operator is the Caputo with order 0&lt;\u03b1&lt;2. The problem also constitutes a class of examples of the Cauchy problem of the Bagley\u2013Torvik equation with variable coefficients. For proving the existence and uniqueness of the solution of the given problem, the contraction mapping principle is utilized. Furthermore, a numerical method and an algorithm are developed for obtaining the approximate solution. Also, convergence analyses are studied, and simulations on some test problems are given. It is shown that the proposed method and the algorithm are easy to implement on a computer and efficient in computational time and storage.<\/jats:p>","DOI":"10.3390\/axioms13090627","type":"journal-article","created":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T03:03:37Z","timestamp":1726196617000},"page":"627","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On the Existence, Uniqueness and a Numerical Approach to the Solution of Fractional Cauchy\u2013Euler Equation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3943-1732","authenticated-orcid":false,"given":"Nazim I.","family":"Mahmudov","sequence":"first","affiliation":[{"name":"Department of Mathematics, Eastern Mediterranean University, North Cyprus, via Mersin 10, 99628 Famagusta, Turkey"},{"name":"Research Center of Econophysics, Azerbaijan State University of Economics (UNEC), Istiqlaliyyat Str. 6, Baku 1001, Azerbaijan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3446-1521","authenticated-orcid":false,"given":"Suzan","family":"Cival Buranay","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Eastern Mediterranean University, North Cyprus, via Mersin 10, 99628 Famagusta, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4277-9283","authenticated-orcid":false,"given":"Mtema James","family":"Chin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Eastern Mediterranean University, North Cyprus, via Mersin 10, 99628 Famagusta, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Touma, R., and Zeidan, D. 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