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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 ρ-convex are derived. It is observed that the obtained inequalities are generalizations of some results in the literature.

Some inequalities obtained by fractional integrals of positive real orders