Fractional integral operators and the multiindex Mittag-Leffler functions. (English) Zbl 1250.26007

Purohit, S. D.; Kalla, S. L.; Suthar, D. L.

Sci., Ser. A, Math. Sci. (N.S.) 21, 87-96 (2011).

Summary: The aim of this paper is to study some properties of multiindex Mittag-Leffler type function \(E_{(1/\rho j),(\mu j)}(z)\) introduced by V. Kiryakova [J. Comput. J. Comput. Appl. Math. 118, No. 1–2, 241–259 (2000; Zbl 0966.33011)]. Here we establish certain theorems which provide the image of this function under the Saigo’s fractional integral operators. The results derived are of general character and give rise to a number of known results in the theory of multiindex Mittag-Leffler functions.

MSC:

26A33	Fractional derivatives and integrals
33E12	Mittag-Leffler functions and generalizations
33C20	Generalized hypergeometric series, \({}_pF_q\)

Keywords:

Mittag-Leffler function; fractional integral operators

Citations:

Zbl 0966.33011