Perturbed F-Metric Spaces: New Fixed Point Results with Applications to Caputo Fractional Initial Value Problems

The primary objective of this study is to establish some new fixed point results in the framework of perturbed F-metric spaces. Specifically, we develop fixed point theorems for three classes of contractions: Banach-type, rational-type, and interpolative contractions. To demonstrate the validity and applicability of the obtained results, some nontrivial examples are provided. Moreover, our findings yield various consequences that extend existing results in both F-metric spaces and perturbed metric spaces. As an application of the main result, we examine the existence of solutions for a Caputo fractional initial value problem.