Integral representation of the four-parametric generalized Mittag-Leffler function

作者: S. Rogosin , A. Koroleva

DOI: 10.1007/S10986-010-9090-4

关键词:

摘要: In this paper, we give a new integral representation of the four-parametric generalized Mittag-Leffler function introduced and studied by Djrbashian (Dzherbashian). The representation, obtained in contains an iterated integral, wherein internal is Cauchy-type external one simple improper along so-called Hankel path. also values special Wright functions.

参考文章(17)
Tilak Raj Prabhakar, A SINGULAR INTEGRAL EQUATION WITH A GENERALIZED MITTAG LEFFLER FUNCTION IN THE KERNEL The Yokohama mathematical journal = 横濱市立大學紀要. D部門, 数学. ,vol. 19, pp. 7- 15 ,(1971)
A. M. Sedletskii, On Zeros of Functions of Mittag--Leffler Type Mathematical Notes. ,vol. 68, pp. 602- 613 ,(2000) , 10.1023/A:1026671508108
A.Y. Popov, A.M. Sedletskii, Zeros distribution of Mittag-Leffler functions Doklady Mathematics. ,vol. 67, pp. 336- 339 ,(2003)
Oleg Igorevich Marichev, Stefan G Samko, Anatoly A Kilbas, Fractional Integrals and Derivatives: Theory and Applications ,(1993)
Hari M Srivastava, Anatoly A Kilbas, Juan J Trujillo, Theory and Applications of Fractional Differential Equations ,(2006)
A. A. Kilbas, A. A. Koroleva, Integral transform with the extended generalized Mittag‐Leffler function Mathematical Modelling and Analysis. ,vol. 11, pp. 173- 186 ,(2006) , 10.3846/13926292.2006.9637311
Anatoly A. Kilbas, Megumi Saigo, R. K. Saxena, GENERALIZED MITTAG-LEER FUNCTION AND GENERALIZED FRACTIONAL CALCULUS OPERATORS Integral Transforms and Special Functions. ,vol. 15, pp. 31- 49 ,(2004) , 10.1080/10652460310001600717
A. M. Sedletskii, Nonasymptotic Properties of Roots of a Mittag-Leffler Type Function Mathematical Notes. ,vol. 75, pp. 372- 386 ,(2004) , 10.1023/B:MATN.0000023316.90489.FE
Anatoly A. Kilbasi, Megumi Saigo, On mittag-leffler type function, fractional calculas operators and solutions of integral equations Integral Transforms and Special Functions. ,vol. 4, pp. 355- 370 ,(1996) , 10.1080/10652469608819121