Some inequalities obtained by fractional integrals of positive real orders

Abstract

The primary objective of this study is to handle new generalized Hermite-Hadamard type inequalities with the help of the Katugampola fractional integral operator, which generalizes the Hadamard and Riemann-Liouville fractional integral operators into one system. In order to do this, a new fractional integral identity is obtained. Then, by using this identity, some inequalities for the class of functions whose derivatives in absolute values at certain powers are rho-convex are derived. It is observed that the obtained inequalities are generalizations of some results in the literature.