On Fractional Calculus Operators and the Basic Analogue of Generalized Mittag-Leffler Function

被引：0

作者：

Bhadana, Krishna Gopal ^{[1
]}

Meena, Ashok Kumar ^{[2
]}

机构：

[1] SPC Govt Coll, Dept Math, Ajmer 305001, Rajasthan, India

[2] Maharshi Dayanand Saraswati Univ, Dept Math, Ajmer 305009, Rajasthan, India

来源：

COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS | 2022年 / 13卷 / 03期

关键词：

Saigo's fractional q-calculus operator; Generalized q-Mittag-Leffler function; q-gamma function; q-shifted factorial and basic hypergeometric series; Q-INTEGRALS;

D O I：

10.26713/cma.v13i3.1854

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, we have derived some unified image formulas of the generalized q-Mittag-Leffler function under fractional calculus operators. We have derived the integral and derivative formulas of Saigo's for the generalized q-Mittag-Leffler function in terms of basic hypergeometric series 2 Phi(1)[ a, b; c vertical bar q, z] and with the help of main results we have obtained the known formulas of the generalized q-Mittag-Leffler function such as Riemann-Liouville fractional integral & derivatives. The Kober and Weyl integrals of the generalized q-Mittag-Leffler function are also obtained as special cases.

引用

页码：835 / 842

页数：8

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