{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T18:51:27Z","timestamp":1790189487406,"version":"4.1.0"},"reference-count":49,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,7,2]],"date-time":"2018-07-02T00:00:00Z","timestamp":1530489600000},"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 paper, we study C\u03b6-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in terms of standard calculus, so we must involve local fractional derivatives. We have generalized the C\u03b6-calculus on the generalized Cantor sets known as middle-\u03be Cantor sets. We have suggested a calculus on the middle-\u03be Cantor sets for different values of \u03be with 0&lt;\u03be&lt;1. Differential equations on the middle-\u03be Cantor sets have been solved, and we have presented the results using illustrative examples. The conditions for super-, normal, and sub-diffusion on fractal sets are given.<\/jats:p>","DOI":"10.3390\/e20070504","type":"journal-article","created":{"date-parts":[[2018,7,2]],"date-time":"2018-07-02T10:56:52Z","timestamp":1530529012000},"page":"504","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":46,"title":["Diffusion on Middle-\u03be Cantor Sets"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5008-0163","authenticated-orcid":false,"given":"Alireza","family":"Khalili Golmankhaneh","sequence":"first","affiliation":[{"name":"Department of Physics, Urmia Branch, Islamic Azad University, Urmia, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1491-1820","authenticated-orcid":false,"given":"Arran","family":"Fernandez","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali","family":"Khalili Golmankhaneh","sequence":"additional","affiliation":[{"name":"Young Researchers and Elite Club, 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, Cankaya University, Ankara 06530, Turkey"},{"name":"Institute of Space Sciences, P.O. 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