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

Serkan Araci, Gauhar Rahman, Abdul Ghaffar, Azeema and Kottakkaran Sooppy Nisar
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Serkan Araci: Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, Gaziantep TR-27410, Turkey
Gauhar Rahman: Department of Mathematics, Shaheed Benazir Bhutto University, Sharingal, Upper Dir 18000, Pakistan
Abdul Ghaffar: Department of Mathematical Science, BUITEMS, Quetta 87300, Pakistan
Azeema: Department of Mathematics, SBK Women University, Quetta 87300, Pakistan
Kottakkaran Sooppy Nisar: Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia

Mathematics, 2019, vol. 7, issue 3, 1-14

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.

Keywords: extended Mittag-Leffler function; Wright-type hypergeometric functions; extended Wright-type hypergeometric functions; statistical distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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