Articles
Kyungpook Mathematical Journal 2019; 59(1): 125-134
Published online March 31, 2019
Copyright © Kyungpook Mathematical Journal.
Pathway Fractional Integral Formulas Involving Extended Mittag-Leffler Functions in the Kernel
Gauhar Rahman, Kottakkaran Sooppy Nisar, Junesang Choi*, Shahid Mubeen, Muhammad Arshad
Department of Mathematics, International Islamic University, Islamabad, Pakistan
e-mail : gauhar55uom@gmail.com
Department of Mathematics, College of Arts and Science-Wadi Al dawser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
e-mail : ksnisar1@gmail.com and n.sooppy@psau.edu.sa
Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea
e-mail : junesang@mail.dongguk.ac.kr
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
e-mail : smjhanda@gmail.com
Department of Mathematics, International Islamic University, Islamabad, Pakistan
e-mail : marshad_zia@yahoo.com
Received: January 23, 2017; Accepted: September 29, 2017
Since the Mittag-Leffler function was introduced in 1903, a variety of extensions and generalizations with diverse applications have been presented and investigated. In this paper, we aim to introduce some presumably new and remarkably different extensions of the Mittag-Leffler function, and use these to present the pathway fractional integral formulas. We point out relevant connections of some particular cases of our main results with known results.
Keywords: gamma function, beta function, extended Mittag-Leffler functions, pathway integral operator.