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In this paper, a new class of functions, namely, exponentially  α , h − m − p -convex functions is introduced to unify various classes of functions already defined in the subject of convex analysis. By using this class of functions, generalized versions of well known fractional integral inequalities of Hadamard and Fejér–Hadamard type are obtained. The results of this paper generate fractional integral inequalities of Hadamard and Fejér–Hadamard type for various types of convex and exponentially convex functions simultaneously.

New Generalized Riemann–Liouville Fractional Integral Versions of Hadamard and Fejér–Hadamard Inequalities