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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.28 no.1 Antofagasta May 2009

http://dx.doi.org/10.4067/S0716-09172009000100003 

Proyecciones Journal of Mathematics
Vol. 28, No 1, pp. 27—34, May 2009.
Universidad Católica del Norte
Antofagasta - Chile


SOME REMARKS ON GENERALIZED MITTAG-LEFFLER FUNCTION


AJAY K. SHUKLA1
JYOTINDRA C. PRAJAPATI2

1 S. V. National Institute Of Technology, India.
2 Charotar Institute Of Technology, India.


Correspondencia a:


Abstract
The principal aim of the paper is to establish the function and its properties by using Fractional Calculus. We also obtained some integral representations of the function which is recently introduced by Shukla and Prajapati[6].


Key Words : Fractional integral operators; fractional differential operators; generalized Mittag-Leffler function; integral representation.
2000 Mathematics Subject Classification : 33E12; 26A33;44A45.

REFERENCES
[1] A. A. Kilbas, M. Saigo and R. K. Saxena, Generalized Mittag-Leffler function and generalized fractional calculus operators, Integral Transforms Spec. Funct., 15, pp. 31-49,         [ Links ](2004).
[2] K. S. Miller and B. Ross, An introduction to fractional calculus and fractional differential equations. Wiley- New York,         [ Links ](1993).
[3] G. M. Mittag-Leffler, Sur la nouvelle fonction Ea(x), C. R. Acad. Sci. Paris 137, pp. 554—558,         [ Links ](1903).
[4] T. R. Prabhakar, On a set of polynomials suggested by Laguerre polynomials, Pacific J. Math., 35 (1), pp. 213-219,         [ Links ](1970).
[5] E. D. Rainville, Special Functions, Macmillan- New York,         [ Links ](1960).
[6] A. K. Shukla and J. C. Prajapati, On a generalization of Mittag-Leffler function and its properties. J. Math. Anal. Appl. 336, pp. 797—811,         [ Links ](2007).
[7] _____, On a Generalized Mittag-Leffler type function and generated integral operator, Article in press, Math. Sci. R         [ Links ]es. J.
[8] _____, Decomposition and properties of Generalized Mittag-Leffler Function, Communicated for Public         [ Links ]ation.
[9] A. Wiman, Über den fundamental Satz in der Theorie der Funktionen Eα(x), Acta Math. 29, pp. 191—201, (1905).
        [ Links ]

AJAY K. SHUKLA
Department of Mathematics
S. V. National Institute of Technology
Surat-395 007
India
e-mail : ajayshukla2@rediffmail.com

JYOTINDRA C. PRAJAPATI
Department of Mathematics
Charotar Institute of Technology
Changa
Anand-388 421
India
e-mail : jyotindra18@rediffmail.com

Received : January 2008. Accepted : March 2009

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