@article{Khan2022, 
author = {Muhammad Bilal Khan and Hatim Ghazi Zaini and Jorge E. Macías-Díaz and Savin Treanțǎ and Mohamed S. Soliman},
title = {Some integral inequalities in interval fractional calculus for left and right coordinated interval-valued functions},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {6},
pages = {10454-10482},
keywords = {coordinated left and right convex interval-valued functions, double interval Riemann-Liouville-type integrals, Hermite-Hadamard type inequalities},
url = {https://www.sciopen.com/article/10.3934/math.2022583},
doi = {10.3934/math.2022583},
abstract = {Integral inequalities play a crucial role in both theoretical and applied mathematics. Because of the relevance of these notions, we have discussed a new class of introduced generalized convex function called as coordinated left and right convex interval-valued function (coordinated LR-convex IVF) using the pseudo-order relation (             ≤              p      ). On interval space, this order relation is defined. First, a pseudo-order relation is used to show Hermite-Hadamard type inequality (HH type inequality) for coordinated LR-convex IVF. Second for coordinated LR-convex IVF, Some HH type inequalities are also derived for the product of two coordinated LR-convex IVFs. Furthermore, we have demonstrated that our conclusions cover a broad range of new and well-known inequalities for coordinated LR-convex IVFs and their variant forms as special instances which are defined by Zhao et al. and Budak et al. Finally, we have shown that the inclusion relation "   ⊇" confidents to the pseudo-order relation "             ≤              p      " for coordinated LR-convex IVFs. The concepts and methodologies presented in this study might serve as a springboard for additional research in this field, as well as a tool for investigating probability and optimization research, among other things.}
}