On a Unified Mittag-Leffler Function and Associated Fractional Integral Operator
Keyword(s):
The aim of this paper is to unify the extended Mittag-Leffler function and generalized Q function and define a unified Mittag-Leffler function. Both the extended Mittag-Leffler function and generalized Q function can be obtained from the unified Mittag-Leffler function. The Laplace, Euler beta, and Whittaker transformations are applied for this function, and generalized formulas are obtained. These formulas reproduce integral transformations of various deduced Mittag-Leffler functions and Q function. Also, the convergence of this unified Mittag-Leffler function is proved, and an associated fractional integral operator is constructed.
2021 ◽
Vol 500
(1)
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pp. 125169
2009 ◽
Vol 80
(2)
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pp. 324-334
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2019 ◽
Vol 113
(3)
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pp. 2407-2420
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Keyword(s):
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