Journal of the
Korean Mathematical Society JKMS

During the past four decades or so, due mainly to a wide range of applications from natural sciences to social sciences, the so-called fractional calculus has attracted an enormous attention of a large number of researchers. Many fractional calculus operators, especially, involving various special functions, have been extensively investigated and widely applied. Here, in this paper, in a systematic manner, we aim to establish certain image formulas of various fractional integral operators involving diverse types of generalized hypergeometric functions, which are mainly expressed in terms of Hadamard product. Some interesting special cases of our main results are also considered and relevant connections of some results presented here with those earlier ones are also pointed out.

Keywords: generalized fractional calculus operators, generalized beta functions of various kinds, generalized hypergeometric functions of various kinds, Hadamard product, incomplete gamma functions, generalized incomplete hypergeometric functions, Appell's hypergeo

MSC numbers: Primary 26A33, 33E20, 33C45; Secondary 33C60, 33C70