A parametrized approach to generalized fractional integral inequalities: Hermite–Hadamard and Maclaurin variants

Abstract

This paper introduces a novel parametrized integral identity that forms the basis for deriving a comprehensive class of generalized fractional integral inequalities. Building on recent advancements in fractional calculus, particularly in conformable fractional integrals, our approach offers a unified framework for various known inequalities. The novelty of this work lies in its ability to generate new and more general inequalities, including Hermite–Hadamard-, Maclaurin-, and corrected Maclaurin-type inequalities, by selecting specific parameter values. These results extend the scope of fractional integral inequalities and provide new insights into their structure. To demonstrate the practical applicability and accuracy of the theoretical findings, we present a detailed numerical example along with graphical representations.

Keywords

• Conformable fractional integral operators
• Maclaurin-type inequalities
• Corrected Maclaurin-type inequalities
• Hermite–Hadamard-type inequalities
• Convex functions