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On fractional integration formulae for Aleph functions (CROSBI ID 170786)

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Saxena, Ram Kishore ; Poganj, Tibor On fractional integration formulae for Aleph functions // Applied mathematics and computation, 218 (2011), 3; 985-990. doi: 10.1016/j.amc.2011.03.026

Podaci o odgovornosti

Saxena, Ram Kishore ; Poganj, Tibor

engleski

On fractional integration formulae for Aleph functions

This paper is devoted to the study of a new special function, which is called, according to the symbol used to represent this function, as an Aleph function. This function is an extension of the I–function, which itself is a generalization of the well–known and familiar G and H–functions in one variable. In this paper, a notation and complete definition of the Aleph function will be presented. Fractional integration of the Aleph functions, in which the argument of the Aleph function contains a factor $t^λ(1-t)^μ, λ, μ>0$, will be investigated. The results derived are of most general character and include many results given earlier by various authors including Kilbas [10], Kilbas and Saigo [11] and Galué [6] and others. The results obtained form the key formulæ for the results on various potentially useful special functions of physical and biological sciences and technology available in the literature.

H–function; I–function; Aleph–function; Mellin–Barnes type integrals; Riemann–Liouville fractional integral; Mittag–Leffler functions

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Podaci o izdanju

218 (3)

2011.

985-990

objavljeno

0096-3003

10.1016/j.amc.2011.03.026

Povezanost rada

Matematika

Poveznice
Indeksiranost