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Abstract Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named ( k , s ) $(k,s)$ -Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

Abstract We aim to present some new Pólya-Szegö type inequalities associated with Hadamard k-fractional integral operators, which are also used to derive some Chebyshev type integral inequalities. Further we apply some of the results presented here to a function which is bounded by the Heaviside functions.