A class of fractional integral operators with multi-index Mittag-Leffler \(k\)-function and Bessel \(k\)-function of first kind

Volume 22, Issue 3, pp 266--281 http://dx.doi.org/10.22436/jmcs.022.03.06

Publication Date: August 31, 2020 Submission Date: March 17, 2020 Revision Date: April 10, 2020 Accteptance Date: June 15, 2020

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Authors

Rana Safdar Ali - Department of Mathematics, University of Sargodha, Sargodha, Pakistan. Shahid Mubeen - Department of Mathematics, University of Sargodha, Sargodha, Pakistan. Muhammad Mumtaz Ahmad - Department of Mathematics, University of Sargodha, Sargodha, Pakistan.

Abstract

In this paper, we discuss the multi-index Mittag Leffler \(k\)-function and Bessel \(k\)-function of the first kind in fractional calculus. We investigate fractional integral operators (Saigo's, Erdelyi Kober, Reimann Liouvill, Weyl) and extend with the product of multi-index Mittag Leffler \(k\)-function to the Bessel \(k\)-function of the first kind. Here, we establish new theorems that provide the image of multi-index Mittag Leffler and Bessel \(k\)-functions under these \(k\)-fractional operators. These results are derived in general behave and give several well-known results in the theory of multi-index \(k\)-functions.

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Keywords

• Fractional integral operators
• generalized Mittag-Leffler \(k\)-function
• Bessel \(k\)-function
• classical hypergeometric functions.

MSC

•  45P05
•  33E12
•  33C10
•  33C05

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