In this work introduced new Chebyshev-type integral inequalities of the Katugampola fractional derivative. Using a Milne-type transformation, we obtain a number of mid-point, trapezoidal and Hermite-Hadamard-type inequalities of various classes of convex functions. The results obtained generalize and extend a wide range of known inequalities relating to classical fractional operators. Special cases related to Caputo and Riemann Liouville version of fractional derivatives are also mentioned proving the effectiveness and generality of the offered approach.

Keywords: Katugampola fractional derivative, Milne transformation, fractional inequalities, convex functions, Chebyshev inequality.