Ostrowski type inequalities via the Katugampola fractional integrals

The main aim of this study is to reveal new generalized-Ostrowski-type inequalities using Katugampola fractional integral operator which generalizes Riemann-Liouville and Hadamard fractional integral operators into a single form. For this purpose, at first, a new fractional integral identity is generated by the researchers. Then, by using this identity, some inequalities for the class of functions whose certain powers of absolute values of derivatives are p-convex are derived. Some applications to special means for positive real numbers are also given. It is observed that the obtained inequalities are generalizations of some well known results.