Some remarks on generalized mittag-leffler function
DOI:
https://doi.org/10.4067/S0716-09172009000100003Keywords:
Fractional integral operators, Fractional differential operators, Generalized Mittag-Leffler function, Integral representation.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].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, (2004).
[2] K. S. Miller and B. Ross, An introduction to fractional calculus and fractional differential equations. Wiley- New York, (1993).
[3] G. M. Mittag-Leffler, Sur la nouvelle fonction Ea(x), C. R. Acad. Sci. Paris 137, pp. 554—558, (1903).
[4] T. R. Prabhakar, On a set of polynomials suggested by Laguerre polynomials, Pacific J. Math., 35 (1), pp. 213-219, (1970).
[5] E. D. Rainville, Special Functions, Macmillan- New York, (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, (2007).
[7] , On a Generalized Mittag-Leffler type function and generated integral operator, Article in press, Math. Sci. Res. J.
[8] , Decomposition and properties of Generalized Mittag-Leffler Function, Communicated for Publication.
[9] A. Wiman, Uber den fundamental Satz in der Theorie der Funktionen Eα(x), Acta Math. 29, pp. 191—201, (1905).
[2] K. S. Miller and B. Ross, An introduction to fractional calculus and fractional differential equations. Wiley- New York, (1993).
[3] G. M. Mittag-Leffler, Sur la nouvelle fonction Ea(x), C. R. Acad. Sci. Paris 137, pp. 554—558, (1903).
[4] T. R. Prabhakar, On a set of polynomials suggested by Laguerre polynomials, Pacific J. Math., 35 (1), pp. 213-219, (1970).
[5] E. D. Rainville, Special Functions, Macmillan- New York, (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, (2007).
[7] , On a Generalized Mittag-Leffler type function and generated integral operator, Article in press, Math. Sci. Res. J.
[8] , Decomposition and properties of Generalized Mittag-Leffler Function, Communicated for Publication.
[9] A. Wiman, Uber den fundamental Satz in der Theorie der Funktionen Eα(x), Acta Math. 29, pp. 191—201, (1905).
How to Cite
[1]
A. K. Shukla and J. C. Prajapati, “Some remarks on generalized mittag-leffler function”, Proyecciones (Antofagasta, On line), vol. 28, no. 1, pp. 27-34, 1.
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