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

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 hypergeomet...

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Bibliographic Details
Published in:Communications in Mathematics and Applications 2022-01, Vol.13 (3), p.835-842
Main Authors: Bhadana, Krishna Gopal, Meena, Ashok Kumar
Format: Article
Language:English
Subjects:
Calculus
Derivatives
Fractional calculus
Integrals
Mathematics
Operators (mathematics)
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Summary: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 \(_2\Phi_1 [a,b;c \, | \, q,z]\) 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.
ISSN:0976-5905
0975-8607
DOI:10.26713/cma.v13i3.1854