Harmonic Inequalities Associated With Left- and Right-Sided Fractional Integral Operators Pertaining Exponential Kernels With Applications

We derive the left- and right-sided fractional Hermite–Hadamard (H–H)-type inequalities for harmonic convex mappings from the left- and right-sided fractional integral operators possessing exponential kernels. In addition, we introduce two variants of fractional equalities that are further deployed with the idea differentiable harmonic convex mappings to explore refine fractional bounds for trapezoid and midpoint-type integral inequalities. We use Power-mean, Hölder’s, and improved Hölder inequality to derive new and refined fractional inequalities. In addition, we make the important connections between the obtained results and those classical integrals very clear. Strong visual illustrations make it evident how accurate and superior the provided technique is. The study includes several applications of special means and numerical quadrature rules. Our results generalize and extend some existing ones in the literature.