Reverse fractional integral inclusions and generic ${\eta }_{\hslash }$ interval-valued convexity

This paper presents the development of reverse Minkowski and reverse Hölder's fractional integral inclusions. We propose a generic class of ${\eta }_{\hslash }$ interval-valued $(\mathrm{I}.\mathrm{V})$ convex functions, which unifies various existing classes. Additionally, we obtain a discrete Jensen-type inclusion within this convexity setup. By leveraging this advanced convexity structure together with tempered fractional integral operators, we derive new Hermite–Hadamard ( $\mathrm{H}$- $\mathrm{H}$)-type, Fejér- $\mathrm{H}$- $\mathrm{H}$-type, and other fractional inclusions. Moreover, we explore the broader significance of our results, supporting them with graphical visualizations. The applications of our results are demonstrated through average value computations.