Communications of the
Korean Mathematical Society CKMS

In this paper, we aim at establishing a generalized fractional integral version of Gr\"uss type integral inequality by making use of the Gauss hypergeometric function fractional integral operator. Our main result, being of a very general character, is illustrated to specialize to yield numerous interesting fractional integral inequalities including some known results.

Keywords: amma function, Gr\"uss integral inequality and Gr\"uss type integral inequalities, Gauss hypergeometric function, Saigo, Erd\'elyi-Kober and Riemann-Liouville type fractional integral operators{Gamma function, Gr\"uss integral inequality and Gr\"uss type

MSC numbers: Primary 33B15, 33B99; Secondary 33C05, 33C15, 33C20, 44A20, 26A33