A class of fractional integral operators with multi-index Mittag-Leffler \(k\)-function and Bessel \(k\)-function of first kind
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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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ISRP Style
Rana Safdar Ali, Shahid Mubeen, Muhammad Mumtaz Ahmad, A class of fractional integral operators with multi-index Mittag-Leffler \(k\)-function and Bessel \(k\)-function of first kind, Journal of Mathematics and Computer Science, 22 (2021), no. 3, 266--281
AMA Style
Ali Rana Safdar, Mubeen Shahid, Ahmad Muhammad Mumtaz, A class of fractional integral operators with multi-index Mittag-Leffler \(k\)-function and Bessel \(k\)-function of first kind. J Math Comput SCI-JM. (2021); 22(3):266--281
Chicago/Turabian Style
Ali, Rana Safdar, Mubeen, Shahid, Ahmad, Muhammad Mumtaz. "A class of fractional integral operators with multi-index Mittag-Leffler \(k\)-function and Bessel \(k\)-function of first kind." Journal of Mathematics and Computer Science, 22, no. 3 (2021): 266--281
Keywords
- Fractional integral operators
- generalized Mittag-Leffler \(k\)-function
- Bessel \(k\)-function
- classical hypergeometric functions.
MSC
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