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Since Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903, due to its usefulness and diverse applications, a variety and large number of its extensions (and generalizations) and variants have been presented and investigated. In this sequel, we aim to introduce a new extension of the Mittag-Leffler function by using a known extended beta function. Then we investigate ceratin useful properties and formulas associated with the extended Mittag-Leffler function such as integral representation, Mellin transform, recurrence relation, and derivative formulas. We also introduce an extended Riemann-Liouville fractional derivative to present a fractional derivative formula for a known extended Mittag-Leffler function, the result of which is expressed in terms of the new extended Mittag-Leffler functions.
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참고문헌 (32)
참고문헌 신청
M. A. Chaudhry / 2004 / Extended hypergeometric and confluent hypergeometric functions / Appl. Math. Comput. 159(2):589~602
J. Choi / 2016 / A note on fractional integral operator associated with multiindex Mittag-Leffler functions / Filomat 30(7):1931~1939
J. Choi / 2015 / Solutions of generalized fractional kinetic equations involving Aleph functions / Math. Commun. 20(1):113~123
C. Fox / 1928 / The asymptotic expansion of generalized hypergeometric functions / Proc. London Math. Soc. 27(5):389~400
R. Gorenflo / 1998 / On the generalized Mittag-Leffler type functions / Integral Transform. Spec. Funct. 7(3-4):215~224
J. Choi / 2016 / A note on fractional integral operator associated with multiindex Mittag-Leffler functions / Filomat 30(7):1931~1939
J. Choi / 2015 / Solutions of generalized fractional kinetic equations involving Aleph functions / Math. Commun. 20(1):113~123
C. Fox / 1928 / The asymptotic expansion of generalized hypergeometric functions / Proc. London Math. Soc. 27(5):389~400
R. Gorenflo / 1998 / On the generalized Mittag-Leffler type functions / Integral Transform. Spec. Funct. 7(3-4):215~224
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