Research Article On Multivalued Hybrid Contractions with Applications Monairah Alansari, 1 Shehu Shagari Mohammed , 2 Akbar Azam , 3 and Nawab Hussain 1 1 Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia 2 Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Nigeria 3 Department of Mathematics, COMSATS University, Chak Shahzad, Islamabad 44000, Pakistan Correspondence should be addressed to Shehu Shagari Mohammed; shagaris@ymail.com Received 11 May 2020; Accepted 18 June 2020; Published 11 July 2020 Guest Editor: Antonio Francisco Roldan Lopez de Hierro Copyright © 2020 Monairah Alansari 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. Recently, a notion of b-hybrid contraction for single-valued mappings in the framework of b-metric spaces which unify and improve several significant existing results in the corresponding literature was introduced. This paper presents a multivalued generalization for such contraction. Moreover, one of our obtained results is applied to analyze some solvability conditions of Fredholm-type integral inclusions. Nontrivial examples are also provided to support the assertions of our theorems. 1. Introduction The Banach contraction principle is the first most well- known, simple, and versatile classical result in fixed point theory with metric space structure. More than a handful of literature embraces applications and generalizations of this principle from different perspectives, for example, by weak- ening the hypotheses, employing different mappings and var- ious forms of metric spaces. In this context, the work of Rhoades [1] is useful for visiting important modifications of Banach-type contractive definitions. In 1969, Nadler [2] gave a generalization of the Banach contraction principle for mul- tivalued contraction mappings by using the Hausdorff metric and established the first fixed point theorem for multivalued mappings defined on metric space. Since then, a number of generalizations in diverse frames of Nadler’s fixed point result have been investigated by several authors (see, for example, [3–9] and references therein). The analysis of new spaces and their properties has been an interesting topic among the mathematical research com- munity. In this direction, the notion of b-metric spaces is presently thriving. The idea commenced with the work of Bakhtin [10] and Bourbaki [11]. Thereafter, Czerwik [12] gave a postulate which is weaker than the classical triangle inequality and formally established a b-metric space with a view of improving the Banach fixed point theorem. Mean- while, the notion of b-metric spaces is gaining enormous gen- eralizations (see, for example, [8, 13–15]). For a recent short survey on basic concepts and results in fixed point theory in the framework of b-metric spaces, we refer the interested reader to Karapinar [16]. On similar development, one of the active branches of fixed point theory that is also currently drawing the attentions of researchers is the study of hybrid contractions. The concept has been viewed in two directions; viz., first, hybrid contraction deals with contractions involv- ing both single-valued and multivalued mappings, and the second merges linear and nonlinear contractions. Recently, Karapinar and Fulga [17] introduced a new notion of b- hybrid contraction in the frame of b-metric space and stud- ied the existence and uniqueness of fixed points for such contraction. Their ideas merged several existing results in the corresponding literature. Interestingly, hybrid fixed point theory has potential applications in functional inclu- sions, optimization theory, fractal graphics, discrete dynam- ics for set-valued operators, and other areas of nonlinear functional analysis. For some work on this line, the reader may consult [17–21]. Integral inclusions arise in several problems in mathemati- cal physics, control theory, critical point theory for nonsmooth energy functionals, differential variational inequalities, fuzzy set arithmetic, traffic theory, etc. (see, for instance, [22–24]). Usually, the first most concerned problem in the study of Hindawi Journal of Function Spaces Volume 2020, Article ID 8401403, 12 pages https://doi.org/10.1155/2020/8401403