On the generalized Kober type fractional q-integral operator involving the basic analogue of the generalized hypergeometric function Sobre el operador q-integral fraccional generalizado de tipo Kober que envuelve la análoga básica de la función hipergeométrica generalizada

Abstract

This paper aims to apply the generalized fractional q-integral operator of the Kober type established by Castillo and Galué, to the basic analogue of the generalized hypergeometric function. Using the series representation of the operator and the basic analogue of the generalized hypergeometric function, a new result is obtained, which by making appropriate changes in its parameters, is verified to contain generalized forms of the q-fractional integrals of the basic hypergeometric functions e_q (x),E_q (x),J_ν^((1)) (x;q),J_ν^((2)) (x;q),L_n^α (x;q),P_n^((α,β)) (x;q), W_n (x;b,q),S_n (x;p,q) and several elementary q-functions. Such results constitute a new table of integrals, which generalizes those established by other researchers.