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In this article, generalized versions of the  k -fractional Hadamard and Fejér-Hadamard inequalities are constructed. To obtain the generalized versions of these inequalities,  k -fractional integral operators including the well-known Mittag-Leffler function are utilized. The class of ( p , h )-convex functions for Hadamard-type inequalities give the generalizations of results which have been proved in literature for  p -convex,  h -convex, and several functions deducible from these two classes.

journal of function spaces

(<math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>p</mi> <mo>,</mo> <mi>h</mi> </math>)-Convex Functions Associated with Hadamard and Fejér-Hadamard Inequalities via <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>k</mi> </math>-Fractional Integral Operators

( p , h )-Convex Functions Associated with Hadamard and Fejér-Hadamard Inequalities via k -Fractional Integral Operators

( $p, h$ )-Convex Functions Associated with Hadamard and Fejér-Hadamard Inequalities via $k$ -Fractional Integral Operators