Fractional integral versions of Hermite-Hadamard type inequality for generalized exponentially convexity

Abstract

In this paper, we establish generalized fractional versions of Hermite-Hadamard inequalities for exponentially (<i>α</i>, <i>h</i> - <i>m</i>)-convex functions, exponentially (<i>h</i> - <i>m</i>)-convex functions and exponentially (<i>α</i>, <i>m</i>)-convex functions. These inequalities arise when using the generalized fractional integral operators containing Mittag-Leffler function via a monotonically increasing function. The presented results hold at the same time for various kinds of convexities and well-known fractional integral operators. Moreover, the established inequalities reproduce several known results which are part of the existing literature.