New developments in fractional Hermite-Hadamard inequalities by means of Harmonic convexity and computational analysis

Abstract

This study explores a mathematical concept called Hermite-Hadamard's inequality with the context of harmonically convexity through the lens of a generalized proportional fractional integral operator.  We then go further by harnessing the power of this fractional integral operator, a suite of refined variants of the Hermite-Hadamard type inequalities emerges, achieved by loosening the stringent harmonically convexity property of the function. To demonstrate the accuracy of our findings, we provide numerical approximations and visually appealing graphs.