Extended Mittag-Leffler function and associated fractional calculus operators

被引：11

作者：

Choi, Junesang ^{[2
]}

Parmar, Rakesh K. ^{[1
]}

Chopra, Purnima ^{[3
]}

机构：

[1] Govt Coll Engn & Technol, Dept Math, Bikaner 334004, Rajasthan, India

[2] Dongguk Univ, Dept Math, Gyeongju 780714, South Korea

[3] Marudhar Engn Coll, Dept Math, Bikaner 334004, Rajasthan, India

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2020年 / 27卷 / 02期

关键词：

Pochhammer symbol; generalized pochhammer symbol; generalized hypergeometric functions; modified Bessel functions; Mittag-Leffler function; Wright hypergeometric function; H-function; generalized Mittag-Leffler function; extended confluent hypergeometric function; Mellin transform; Euler-Beta transform; Laplace transform; Whittaker transform; fractional calculus operators; HYPERGEOMETRIC-FUNCTIONS; GENERATING-FUNCTIONS; SYMBOL;

D O I：

10.1515/gmj-2019-2030

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [H. M. Srivastava, A. cetinkaya and I. Onur Kiymaz, A certain generalized Pochhammer symbol and its applications to hypergeometric functions, Appi. 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.

引用

页码：199 / 209

页数：11

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