Abstract
The appreciation of inequalities in convexity is critical for fractional calculus and its application in a variety of fields. In this paper, we provide a unique analysis based on Hermite-Hadamard inequalities in the context of newly defined class of convexity which is known as left and right harmonically h-convex IVF (left and right H-h-convex IVF), as well as associated integral and fractional inequalities, are addressed by the suggested technique. Because of its intriguing character in the numerical sciences, there is a strong link between fractional operators and convexity. There have also been several exceptional circumstances studied, and numerous well-known Hermite-Hadamard inequalities have been derived for left and right H-h-convex IVF. Moreover, some applications are also presented in terms of special cases which are discussed in this study. The plan's outcomes demonstrate that the approach may be implemented immediately and is computationally simple and precise. We believe, our findings, generalize certain well-known new and classical harmonically convexity discoveries from the literature.