{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,6]],"date-time":"2024-06-06T02:40:20Z","timestamp":1717641620446},"reference-count":27,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,9,6]],"date-time":"2016-09-06T00:00:00Z","timestamp":1473120000000},"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":"Motivated by statistical mechanics contexts, we study the properties of the q-Laplace transform, which is an extension of the well-known Laplace transform. In many circumstances, the kernel function to evaluate certain integral forms has been studied. In this article, we establish relationships between q-exponential and other well-known functional forms, such as Mittag\u2013Leffler functions, hypergeometric and H-function, by means of the kernel function of the integral. Traditionally, we have been applying the Laplace transform method to solve differential equations and boundary value problems. Here, we propose an alternative, the q-Laplace transform method, to solve differential equations, such as as the fractional space-time diffusion equation, the generalized kinetic equation and the time fractional heat equation.<\/jats:p>","DOI":"10.3390\/axioms5030024","type":"journal-article","created":{"date-parts":[[2016,9,6]],"date-time":"2016-09-06T14:10:16Z","timestamp":1473171016000},"page":"24","source":"Crossref","is-referenced-by-count":6,"title":["On the q-Laplace Transform and Related Special Functions"],"prefix":"10.3390","volume":"5","author":[{"given":"Shanoja","family":"Naik","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0104-2355","authenticated-orcid":false,"given":"Hans","family":"Haubold","sequence":"additional","affiliation":[{"name":"Office for Outer Space Affairs, United Nations, Vienna International Centre, Vienna 1400, Austria"}]}],"member":"1968","published-online":{"date-parts":[[2016,9,6]]},"reference":[{"key":"ref_1","unstructured":"Sneddon, I.N. 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