{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T07:06:10Z","timestamp":1763017570743,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2015,9,8]],"date-time":"2015-09-08T00:00:00Z","timestamp":1441670400000},"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>The transfer of heat due to the emission of electromagnetic waves is called thermal radiations. In local fractional calculus, there are numerous contributions of scientists, like Mandelbrot, who described fractal geometry and its wide range of applications in many scientific fields. Christianto and Rahul gave the derivation of Proca equations on Cantor sets. Hao et al. investigated the Helmholtz and diffusion equations in Cantorian and Cantor-Type Cylindrical Coordinates. Carpinteri and Sapora studied diffusion problems in fractal media in Cantor sets. Zhang et al. studied local fractional wave equations under fixed entropy.  In this paper, we are concerned with the exact solutions of wave equations by the help of local fractional Laplace variation iteration method (LFLVIM). We develop an iterative scheme for the exact solutions of local fractional wave equations (LFWEs). The efficiency of the scheme is examined by two illustrative examples.<\/jats:p>","DOI":"10.3390\/e17096229","type":"journal-article","created":{"date-parts":[[2015,9,8]],"date-time":"2015-09-08T11:59:54Z","timestamp":1441713594000},"page":"6229-6237","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["On the Exact Solution of Wave Equations on Cantor Sets"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"first","affiliation":[{"name":"Department of Mathematics Computer Science, Cankaya University, Ankara 06530, Turkey"},{"name":"Institute of Space Sciences, P. O. Box, MG-23, Magurele-Bucharest 76900, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hasib","family":"Khan","sequence":"additional","affiliation":[{"name":"University of Malakand, Chakdara, Dir lower, P. O. Box, Khybar Pakhtunkhwa 18000, Pakistan"},{"name":"Shaheed Benazir Bhutto University, Sheringal, Dir Upper, P. O. Box, Khybar Pakhtunkhwa 18000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6807-6675","authenticated-orcid":false,"given":"Hossien","family":"Jafari","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of South Africa, P. O. Box 392, UNISA 0003, South Africa"},{"name":"Department of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rahmat","family":"Khan","sequence":"additional","affiliation":[{"name":"University of Malakand, Chakdara, Dir lower, P. O. Box, Khybar Pakhtunkhwa 18000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,9,8]]},"reference":[{"key":"ref_1","unstructured":"Mandelbrot, B.B. 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Phys., 2014.","DOI":"10.1155\/2014\/590574"},{"key":"ref_12","first-page":"75","article-title":"A Derivation of Proca Equations on Cantor Sets: A Local Fractional Approach","volume":"3","author":"Christianto","year":"2014","journal-title":"Bull. Math. Sci. Appl."},{"key":"ref_13","first-page":"754248:1","article-title":"Helmholtz and Diffusion Equations Associated with Local Fractional Derivative Operators Involving the Cantorian and Cantor-Type Cylindrical Coordinates, Adv","volume":"2013","author":"Hao","year":"2013","journal-title":"Math. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1002\/zamm.200900376","article-title":"Diffusion Problems in Fractal Media Defined on Cantor Sets","volume":"90","author":"Carpinteri","year":"2010","journal-title":"Z. Angew. Math. Mech."},{"key":"ref_15","first-page":"351057:1","article-title":"Local Fractional Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets","volume":"2013","author":"Yang","year":"2013","journal-title":"Abstr. Appl. Anal."},{"key":"ref_16","first-page":"1","article-title":"Fractional Complex Transform Method for Wave Equations on Cantor Sets within Local Fractional Differential Operator","volume":"1","author":"Su","year":"2013","journal-title":"Adv. Differ. Equ."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/9\/6229\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:48:10Z","timestamp":1760215690000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/9\/6229"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,8]]},"references-count":16,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2015,9]]}},"alternative-id":["e17096229"],"URL":"https:\/\/doi.org\/10.3390\/e17096229","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,9,8]]}}}