{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T16:22:47Z","timestamp":1774282967223,"version":"3.50.1"},"reference-count":52,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,14]],"date-time":"2024-11-14T00:00:00Z","timestamp":1731542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this research paper, we provide a concise overview of fractal calculus applied to fractal sets. We introduce and solve a 2\u03b1-order fractal differential equation with constant coefficients across different scenarios. We propose a uniqueness theorem for 2\u03b1-order fractal linear differential equations. We define the solution space as a vector space with non-integer orders. We establish precise conditions for 2\u03b1-order fractal linear differential equations and derive the corresponding fractal adjoint differential equation.<\/jats:p>","DOI":"10.3390\/axioms13110786","type":"journal-article","created":{"date-parts":[[2024,11,14]],"date-time":"2024-11-14T09:14:31Z","timestamp":1731575671000},"page":"786","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Fractal Differential Equations of 2\u03b1-Order"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5008-0163","authenticated-orcid":false,"given":"Alireza","family":"Khalili Golmankhaneh","sequence":"first","affiliation":[{"name":"Department of Physics, Islamic Azad University, Urmia Branch, Urmia 63896, West Azerbaijan, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6518-8505","authenticated-orcid":false,"given":"Donatella","family":"Bongiorno","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Palermo, 90100 Palermo, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,14]]},"reference":[{"key":"ref_1","unstructured":"Mandelbrot, B.B. 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