Analysis of inclusions using $s$-type convex interval-valued functions via Riemann-Liouville fractional integrals

This paper examines a family of convex interval-valued (IVC) functions using the Riemann-Liouville (RL) integrals. Hermite-Hadamard (HH) and Hermite-Hadamard-Fejér (HHF) type inclusions are developed by employing the $s$-type convexity of interval-valued (Ⅳ) functions. Some inclusions for the product of $s$-type (IVC) functions are also established involving RL integrals. All main results are furthur refined into inclusions and inequalities for $s$-type IVC functions and $s$-type convex point-valued functions, respectively, involving the ordinary integral. In addition, several consequences of the primary results are explored demonstrating the connections between point-valued convex functions, IVC functions, and $s$-type IVC functions. Each key conclusion is validated numerically. The results of this paper might open the path for new avenues in modeling, optimization problems, interval differential equations, and fuzzy Ⅳ functions that involve both discrete and continuous variables simultaneously.