Some new Hadamard-type inequalities via fractional integral operators

Abstract

The article presents new inequalities of Hadamard-type which are obtained using fractional integral operators belonging to a function whose third-order derivative is convex. The proposed Hadamard-type inequalities have the potential for application in various areas where it is required to estimate the properties of functions with a convex third-order derivative. Examples of functions are given based on a comparative analysis of the estimates of the upper bounds of the Hadamard-type inequalities obtained using the classical and extended Hölder inequalities. Finally, applications to special functions are provided.