@article{Nosheen2026, 
author = {Ammara Nosheen and Khuram Ali Khan and Mariam Aslam and Atiq Ur Rehman and Tamador Alihia and Salwa El-Morsy},
title = {Analysis of inclusions using    s-type convex interval-valued functions via Riemann-Liouville fractional integrals},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {1},
pages = {2027-2045},
keywords = {convex functions, fractional integrals, interval-valued functions, integral inclusions, optimization problems, mathematical operators},
url = {https://www.sciopen.com/article/10.3934/math.2026084},
doi = {10.3934/math.2026084},
abstract = {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.}
}