Communications of the
Korean Mathematical Society CKMS

We aim to establish certain Saigo hypergeometric fractional integral formulas for a finite product of the generalized $\mathtt{k}$-Bessel functions, which are also used to present image formulas of several integral transforms including beta transform, Laplace transform, and Whittaker transform. The results presented here are potentially useful, and, being very general, can yield a large number of special cases, only two of which are explicitly demonstrated.

Keywords: $\mathtt{k}$-Pochhammer symbol, $\mathtt{k}$-gamma function, Fox-Wright function, generalized $\mathtt{k}$-Bessel function, Laplace transform, beta transform, Whittaker transform, Saigo hypergeometric fractional integral operators

MSC numbers: Primary 26A33, 33C45; Secondary 33C60, 33C70