Research Article Fixed Point Results for Rational Orbitally (Θ, δ b )-Contractions with an Application Zhenhua Ma, 1 Jamshaid Ahmad , 2 Abdullah Eqal Al-Mazrooei, 2 and Durdana Lateef 3 1 Department of Mathematics and Physics, Hebei University of Architecture, Zhangjiakou 075024, China 2 Department of Mathematics, University of Jeddah, Saudi Arabia 3 Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawwara, Madina 41411, Saudi Arabia Correspondence should be addressed to Jamshaid Ahmad; jamshaid_jasim@yahoo.com Received 6 March 2021; Revised 17 April 2021; Accepted 12 June 2021; Published 29 June 2021 Academic Editor: Huseyin Isik Copyright © 2021 Zhenhua Ma et al. This 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. The purpose of this paper is to define a rational orbitally (Θ, δ b )-contraction and prove some new results in the context of b-metric spaces. Our results extend, generalize, and unify some known results in the literature. As application of our main result, we investigate the solution of Fredholm integral inclusion. We also provide an example to substantiate the advantage and usefulness of obtained results. 1. Introduction The fixed point theory is a very essential tool for nonlinear analysis of solvability of nonlinear integral equations and others. A suitable selection of a generalized and extended metric space allows to get nontrivial conditions guaranteeing the existence of solutions for a considered equation. There- fore, it is necessary to flourish the fixed point theory in vari- ous generalization of metric spaces. One of the famous extensions of metric space is the notion of b-metric space which has been given by Bakhtin [1] in 1989. It was properly defined by Czerwik [2] with the aspect of relaxing triangle inequality in metric spaces in 1993 and proved famous Banach Contraction Principle in this generalized metric space. Khamsi and Hussain [3] discussed the topology of b -metric space and established fixed point results for KKM mappings in metric type spaces. Van An et al. [4] proved the Stone-type theorem on b-metric spaces and obtained a sufficient condition for a b-metric space to be metrizable. On the other, Czerwik [5, 6] introduced set-valued mappings in b-metric spaces and generalized Nadler’s fixed point theo- rem. In 2012, Aydi et al. [7, 8] gave fixed point and common fixed point theorems for set-valued quasicontraction map- pings and set-valued weak ϕ-contraction mappings in the setting of b-metric spaces, respectively. Many authors followed the concept of b-metric space and established impressive results [9–19]. In 2012, Jleli and Samet [20] introduced a new type of contraction named as Θ-contraction and obtained a fixed point result to generalize the celebrated Banach Contraction Principle in Branciari metric spaces. Ali et al. [21] defined multivalued Suzuki-type θ-contractions and obtained some generalized fixed point results. Afterwards, Jleli et al. [22] established a new fixed point theorem for Θ-contraction in the setting of Branciari metric spaces and extended the main result of Jleli and Samet [20]. Recently, Alamri et al. [23] adapted Jleli’s approach to the b-metric space and obtained some generalized fixed point results. For more details in the direction of Θ-contractions, we refer the reader to [21–30]. In this paper, we define the notion of the rational (Θ, δ b )-contraction in b-metric spaces and explore the existence of solutions for certain integral problems of Fredholm type as applications of our main results. We obtain our results by using fixed point theorems for multi- valued mappings, under new contractive conditions, in the setting of complete b-metric spaces. Evidently, the given results generalized some notable results of the literature to b-metric spaces. Hindawi Journal of Function Spaces Volume 2021, Article ID 9946125, 9 pages https://doi.org/10.1155/2021/9946125