Fractional Versions of Hadamard-Type Inequalities for Strongly Exponentially α , h − m -Convex Functions

Abstract

In this article, we prove some fractional versions of Hadamard-type inequalities for strongly exponentially $\left(\alpha ,h-m\right)$ -convex functions via generalized Riemann–Liouville fractional integrals. The outcomes of this paper provide inequalities of strongly convex, strongly $m$ -convex, strongly $s$ -convex, strongly $\left(\alpha ,m\right)$ -convex, strongly $\left(s,m\right)$ -convex, strongly $\left(h-m\right)$ -convex, strongly $\left(\alpha ,h-m\right)$ -convex, strongly exponentially convex, strongly exponentially $m$ -convex, strongly exponentially $s$ -convex, strongly exponentially $\left(s,m\right)$ -convex, strongly exponentially $\left(h-m\right)$ -convex, and exponentially $\left(\alpha ,h-m\right)$ -convex functions. The error estimations are also studied by applying two fractional integral identities.