{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T16:02:10Z","timestamp":1787500930971,"version":"build-2736575974"},"reference-count":22,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2016,1,29]],"date-time":"2016-01-29T00:00:00Z","timestamp":1454025600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on the fractals subset of real-line lies in the fact that they are better at modeling processes with memory effect.<\/jats:p>","DOI":"10.3390\/e18020001","type":"journal-article","created":{"date-parts":[[2016,1,29]],"date-time":"2016-01-29T09:58:48Z","timestamp":1454061528000},"page":"1","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":58,"title":["New Derivatives on the Fractal Subset of Real-Line"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5008-0163","authenticated-orcid":false,"given":"Alireza","family":"Khalili Golmankhaneh","sequence":"first","affiliation":[{"name":"Department of Physics, College of Science, Urmia Branch, Islamic Azad University, Urmia, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Art and Sciences, Cankaya University, Ankara 06530, Turkey"},{"name":"Institute of Space Sciences, P.O. 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Analysis on Fractals, Cambridge University Press.","DOI":"10.1017\/CBO9780511470943"},{"key":"ref_17","unstructured":"Yang, X.-J. (2012). Advanced Local Fractional Calculus and Its Applications, World Science."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2909","DOI":"10.1007\/s10773-012-1169-8","article-title":"On the fractional Hamilton and Lagrange mechanics","volume":"51","author":"Golmankhaneh","year":"2012","journal-title":"Int. J. Theor. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4210","DOI":"10.1007\/s10773-013-1733-x","article-title":"Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line","volume":"52","author":"Golmankhaneh","year":"2013","journal-title":"Int. J. Theor. Phys."},{"key":"ref_20","first-page":"863","article-title":"About Maxwell\u2019s equations on fractal subsets of R3","volume":"11","author":"Golmankhaneh","year":"2013","journal-title":"Cent. Eur. J. 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