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Mathematics 2015, 3(4), 1069-1082; doi:10.3390/math3041069

A Class of Extended Mittag–Leffler Functions and Their Properties Related to Integral Transforms and Fractional Calculus

Department of Mathematics, Government College of Engineering and Technology, Bikaner 334004, India
Academic Editor: Hari M. Srivastava
Received: 30 March 2015 / Revised: 11 October 2015 / Accepted: 26 October 2015 / Published: 6 November 2015
(This article belongs to the Special Issue Recent Advances in Fractional Calculus and Its Applications)
View Full-Text   |   Download PDF [296 KB, uploaded 6 November 2015]

Abstract

In a joint paper with Srivastava and Chopra, we introduced far-reaching generalizations of the extended Gammafunction, extended Beta function and the extended Gauss hypergeometric function. In this present paper, we extend the generalized Mittag–Leffler function by means of the extended Beta function. We then systematically investigate several properties of the extended Mittag–Leffler function, including, for example, certain basic properties, Laplace transform, Mellin transform and Euler-Beta transform. Further, certain properties of the Riemann–Liouville fractional integrals and derivatives associated with the extended Mittag–Leffler function are investigated. Some interesting special cases of our main results are also pointed out. View Full-Text
Keywords: extended Beta function; extended hypergeometric functions; extended confluent hypergeometric function; Mittag–Leffler function; generalized Mittag–Leffler function; Laplace transform; Mellin transform; Euler-Beta transforms; Wright hypergeometric function; Fox H-function; fractional calculus operators extended Beta function; extended hypergeometric functions; extended confluent hypergeometric function; Mittag–Leffler function; generalized Mittag–Leffler function; Laplace transform; Mellin transform; Euler-Beta transforms; Wright hypergeometric function; Fox H-function; fractional calculus operators
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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Parmar, R.K. A Class of Extended Mittag–Leffler Functions and Their Properties Related to Integral Transforms and Fractional Calculus. Mathematics 2015, 3, 1069-1082.

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