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Georgian Mathematical Journal

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Extended Mittag-Leffler function and associated fractional calculus operators

Junesang Choi / Rakesh K. Parmar
  • Corresponding author
  • Department of Mathematics, Government College of Engineering and Technology, Bikaner 334004, Rajasthan State, India
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/ Purnima Chopra
Published Online: 2019-06-21 | DOI: https://doi.org/10.1515/gmj-2019-2030


Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [H. M. Srivastava, A. Çetinkaya and I. Onur Kıymaz, A certain generalized Pochhammer symbol and its applications to hypergeometric functions, Appl. Math. Comput. 226 2014, 484–491] by means of the generalized Pochhammer symbol, we introduce here a new extension of the generalized Mittag-Leffler function. We then systematically investigate several properties of the extended Mittag-Leffler function including some basic properties, Mellin, Euler-Beta, Laplace and Whittaker transforms. Furthermore, certain properties of the Riemann–Liouville fractional integrals and derivatives associated with the extended Mittag-Leffler function are also investigated. Some interesting special cases of our main results are pointed out.

Keywords: Pochhammer symbol; generalized pochhammer symbol; generalized hypergeometric functions; modified Bessel functions; Mittag-Leffler function; Wright hypergeometric function; generalized Mittag-Leffler function; extended confluent hypergeometric function; Mellin transform; Euler-Beta transform; Laplace transform; Whittaker transform; fractional calculus operators

MSC 2010: 26A33; 33E12; 33C05; 33C15; 33C20; 33C65; 33C90


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About the article

Received: 2015-04-22

Revised: 2015-11-30

Accepted: 2016-02-22

Published Online: 2019-06-21

Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2030.

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