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 (α, h − m)-convex functions, exponentially (h − m)-convex functions and exponentially (α, m)-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.

Keywords

• convex function
• hermite-hadamard inequality
• generalized fractional integral operators
• mittag-leffler function