# Hermite-Hadamard's Mid-Point Type Inequalities for Generalized Fractional Integrals

## TL;DR

This paper establishes new Hermite-Hadamard type inequalities for generalized fractional integrals, expanding existing results to broader classes of functions and providing applications to special means.

## Contribution

It introduces novel mid-point inequalities for Katugampola fractional integrals, generalizing previous results and including applications to inequalities involving special means.

## Key findings

- Derived Hermite-Hadamard inequalities for Lipschitzian and convex functions.
- Extended inequalities to generalized fractional integrals like Katugampola.
- Connected inequalities to classical means, broadening their applicability.

## Abstract

Some Hermite-Hadamard's mid-point type inequalities related to Katugampola fractional integrals are obtained where the first derivative of considered mappings is Lipschitzian or convex. Also some mid-point type inequalities are given for Lipschitzian mappings, with the aim of generalizing the results presented in previous works. Finally as an application, some generalized inequalities in connection with special means are provided.