@article{Khan2022, 
author = {Muhammad Bilal Khan and Savin Treanțǎ and Hleil Alrweili and Tareq Saeed and Mohamed S. Soliman},
title = {Some new Riemann-Liouville fractional integral inequalities for interval-valued mappings},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {8},
pages = {15659-15679},
keywords = {L-R J-convex interval-valued mapping, interval Riemann-Liouville fractional integral operator, Hermite-Hadamard inequality, Hermite-Hadamard Fejér inequality},
url = {https://www.sciopen.com/article/10.3934/math.2022857},
doi = {10.3934/math.2022857},
abstract = {The notions of convex mappings and inequalities, which form a strong link and are key parts of classical analysis, have gotten a lot of attention recently. As a familiar extension of the classical one, interval-valued analysis is frequently used in the research of control theory, mathematical economy and so on. Motivated by the importance of convexity and inequality, our aim is to consider a new class of convex interval-valued mappings (I-V⋅Ms) known as left and right (L-R)        J  -convex interval-valued mappings through pseudo-order relation (             ≤              p      ) or partial order relation, because in interval space, both concepts coincide, so this order relation is defined in interval space. By using this concept, first we obtain Hermite-Hadamard (HH-) and Hermite-Hadamard-Fejér (HH-Fejér) type inequalities through pseudo-order relations via the Riemann-Liouville fractional integral operator. Moreover, we have shown that our results include a wide class of new and known inequalities for L-R        J  -convex- I-V⋅Ms and their variant forms as special cases. Under some mild restrictions, we have proved that the inclusion relation "   ⊆" is coincident to pseudo-order relation "             ≤              p      " when the I-V⋅M is L-R        J  -convex or L-R        J  -concave. Results obtained in this paper can be viewed as an improvement and refinement of classical known results.}
}