| Summary: | <i>F</i>-contractions have inspired a branch of metric fixed point theory committed to the generalization of the classical Banach contraction principle. The study of these contractions and <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-fuzzy mappings in <i>b</i>-metric spaces was attempted timidly and was not successful. In this article, the main objective is to obtain common <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-fuzzy fixed point results for <i>F</i>-contractions in <i>b</i>-metric spaces. Some multivalued fixed point results in the literature are derived as consequences of our main results. We also provide a non-trivial example to show the validity of our results. As applications, we investigate the solution for fuzzy initial value problems in the context of a generalized Hukuhara derivative. Our results generalize, improve and complement several developments from the existing literature.
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