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Mathematics 2019, 7(3), 248; https://doi.org/10.3390/math7030248

Fractional Calculus of Extended Mittag-Leffler Function and Its Applications to Statistical Distribution

1
Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, Gaziantep TR-27410, Turkey
2
Department of Mathematics, Shaheed Benazir Bhutto University, Sharingal, Upper Dir 18000, Pakistan
3
Department of Mathematical Science, BUITEMS, Quetta 87300, Pakistan
4
Department of Mathematics, SBK Women University, Quetta 87300, Pakistan
5
Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
*
Author to whom correspondence should be addressed.
Received: 25 December 2018 / Revised: 3 March 2019 / Accepted: 6 March 2019 / Published: 10 March 2019
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Abstract

Several fractional calculus operators have been introduced and investigated. In this sequence, we aim to establish the Marichev-Saigo-Maeda (MSM) fractional calculus operators and Caputo-type MSM fractional differential operators of extended Mittag-Leffler function (EMLF). We also investigate the statistical distribution associated with the EMLF. Finally, we derive some of the particular cases of the main results. View Full-Text
Keywords: extended Mittag-Leffler function; Wright-type hypergeometric functions; extended Wright-type hypergeometric functions; statistical distribution extended Mittag-Leffler function; Wright-type hypergeometric functions; extended Wright-type hypergeometric functions; statistical distribution
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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Araci, S.; Rahman, G.; Ghaffar, A.; Azeema; Nisar, K.S. Fractional Calculus of Extended Mittag-Leffler Function and Its Applications to Statistical Distribution. Mathematics 2019, 7, 248.

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