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Axioms 2016, 5(3), 24; doi:10.3390/axioms5030024

On the q-Laplace Transform and Related Special Functions

1
Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada
2
Office for Outer Space Affairs, United Nations, Vienna International Centre, Vienna 1400, Austria
*
Author to whom correspondence should be addressed.
Academic Editor: Javier Fernandez
Received: 12 July 2016 / Revised: 24 August 2016 / Accepted: 30 August 2016 / Published: 6 September 2016
View Full-Text   |   Download PDF [287 KB, uploaded 6 September 2016]

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–Leffler 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. View Full-Text
Keywords: convolution property; G-transform; Gauss hypergeometric function; generalized kinetic equation; Laplace transform; Mittag–Leffler function; versatile integral convolution property; G-transform; Gauss hypergeometric function; generalized kinetic equation; Laplace transform; Mittag–Leffler function; versatile integral
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Naik, S.R.; Haubold, H.J. On the q-Laplace Transform and Related Special Functions. Axioms 2016, 5, 24.

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