Research Article Fuzzy Fixed Point Results of Fuzzy Mappings on b-Metric Spaces via ðα ∗ , F Þ-Contractions Samina Batul, 1 Dur-e-Shehwar Sagheer, 1 Muhammad Anwar, 1 Hassen Aydi , 2,3,4 and Vahid Parvaneh 5 1 Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan 2 Université de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia 3 China Medical University Hospital, China Medical University, Taichung 40402, Taiwan 4 Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa 5 Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran Correspondence should be addressed to Hassen Aydi; hassen.aydi@isima.rnu.tn and Vahid Parvaneh; zam.dalahoo@gmail.com Received 16 May 2022; Revised 26 June 2022; Accepted 14 July 2022; Published 29 July 2022 Academic Editor: Ivan Giorgio Copyright © 2022 Samina Batul 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. In this manuscript, we establish some fixed point results for fuzzy mappings via ðα ∗ , FÞ -contractions. For validation of the proved results, some nontrivial examples are presented. Few interesting consequences are also stated which authenticate that our results generalize many existing ones in the literature. 1. Introduction Fixed point theory has attained an important and significant role in analysis. The literature of the last four decades orna- mented with results which discover fixed points of self and non-self nonlinear operators in a metric space. This branch of mathematics provides a strong tool for finding out the solution of integral, differential, and eigenvalue equations. Since 1922, the Banach contraction principle (BCP) has become the center of the attention for researchers working in different areas. The eminent Banach contraction principle (BCP) [1] states that for a complete metric space ðΩ, dÞ, each self-mapping η on Ω satisfying d ηξ 1 , ηξ 2 ð Þ ≤ λd ξ 1 , ξ 2 ð Þ,∀ξ 1 , ξ 2 ∈ Ω, where λ ∈ 0, 1 ½ Þ ð1Þ has a unique fixed point. A lot of literature can be found on generalizations and extensions of the famous BCP by changing either the space under consideration or the condition on the mapping. In recent years, various authors presented interesting generaliza- tions of a metric space, for example, uniform space [2, 3], b -metric space [4], C ∗ -algebra valued metric space [5, 6], G p b -metric space [7], and b 2 -metric space [8]. A very interesting generalization of metric space is cone metric space. Gupta and Chauhan [9] presented an analo- gous to the BCP on cone b-metric spaces in 2021. In con- trast, Wardowski [10] extended the Banach contraction to a more generalized form, known as F -contractions, and established a fixed point theorem in complete metric spaces. Furthermore, many mathematicians used F -contractions for the existence of a fixed point, see [11–13]. Nadler’s theorem [14] states that for a complete metric space ðΩ, dÞ, each non- self-mapping η : Ω ⟶ CðΩÞ satisfying H ηξ 1 , ηξ 2 ð Þ ≤ λd ξ 1 , ξ 2 ð Þ,∀ξ 1 , ξ 2 ∈ Ω, where λ ∈ 0, 1 ½ Þ ð2Þ has a fixed point. Here, H denotes the Hausdorff metric defined on CðΩÞ, the set of bounded and closed subsets of Ω. Throughout the article, a b − metric space and a fuzzy fixed point are denoted by a bms and a ffp, respectively. Some important definitions are presented before construct- ing the main results. These definitions are inevitable for next discussion. Hindawi Advances in Mathematical Physics Volume 2022, Article ID 4511632, 8 pages https://doi.org/10.1155/2022/4511632