Research Article Inclusions Involving Interval-Valued Harmonically Co-Ordinated Convex Functions and Raina’s Fractional Double Integrals Bandar Bin Mohsin, 1 Muhammad Uzair Awan , 2 Muhammad Zakria Javed, 2 H¨ useyin Budak , 3 Awais Gul Khan, 2 and Muhammad Aslam Noor 4 1 Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia 2 Department of Mathematics, Government College University, Faisalabad, Pakistan 3 Department of Mathematics, Faculty of Science and Arts, D ¨ uzce University, D¨ uzce, Turkey 4 Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan Correspondence should be addressed to Muhammad Uzair Awan; awan.uzair@gmail.com Received 10 June 2022; Accepted 22 July 2022; Published 20 September 2022 Academic Editor: Xiaolong Qin Copyright © 2022 Bandar Bin Mohsin et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e aim of this article is to obtain some new integral inclusions essentially using the interval-valued harmonically co-ordinated convex functions and κ-Raina’s fractional double integrals. To show the validity of our theoretical results, we also give some numerical examples. 1. Introduction A convex analysis is the branch of mathematics in which we study the properties of convex sets and convex functions. ese classical concepts have a wide range of applications in both pure and applied sciences. For instance, every one is familiar with the role of convexity in the theory of optimization, op- erations research, mathematical economics, theory of means etc. In recent years the classical concepts of the convexity have been extended and generalized in different directions using novel and innovative ideas. For example, Dragomir [1] ex- tended the notion of classical convex functions on the coor- dinates and introduced the class of co-ordinated convex functions. Iscan [2] introduced the notion of harmonically convex functions and observed that this class enjoys some nice properties which the convex functions have. Nikodem [3] introduced the class of interval-valued convex functions and discussed its properties. Zhao et al. [4] introduced the notion of interval-valued harmonically convex functions. For more de- tails, interested readers are referred to the book [5]. Another charming aspect of the theory of convexity is its relation with the theory of inequalities. Many inequalities which are known to us are direct consequences of the applications of the convexity property of the functions. In this regard, one of the most studied results is Hermite-Hadamard’s inequality. is inequality provides us with a necessary and sufficient condition for a function to be convex. It reads as, let Θ: I [℘ 1 , ℘ 2 ]⊆R ⟶ R be a convex function, then Θ ℘ 1 + ℘ 2 2   ≤ 1 ℘ 2 − ℘ 1  ℘ 2 ℘ 1 Θ(x)dx ≤ Θ℘ 1 ( ) + Θ℘ 2 ( ) 2 . (1) is result is one of the most significant results pertaining to the convexity property of the functions which has been studied extensively as well as intensively. In recent years this result has been extended and generalized in different ways using novel and innovative ideas. For example, Dragomir [1] ob- tained a new version of Hermite-Hdamard’s inequality by using the co-ordinated convexity property of the functions. Iscan [2] obtained Hermite-Hadamard’s inequality using the class of harmonic convex functions. Zhao obtained a similar result by using the interval-valued harmonically convex functions. Sarikaya et al. [6] have utilized the concepts of fractional calculus and obtained fractional analogues of Hermite-Hada- mard’s inequality. For some more recent studies regarding Hermite-Hadamard’s inequality and its applications, see [7]. Hindawi Journal of Mathematics Volume 2022, Article ID 5815993, 21 pages https://doi.org/10.1155/2022/5815993