Fixed Point Results in Extended ℱ-Metric Spaces with Applications to Caputo Fractional Differential Equations

The purpose of this research work is to propose and develop the notion of α,ψ-contractions in the setting of extended F-metric spaces and to establish corresponding fixed point results. Using these results, we derive fixed point results for graphic contractions in extended F-metric spaces as well as for mappings in partially ordered extended F-metric spaces. To demonstrate the validity and novelty of the proposed results, a non-trivial example is provided. Moreover, the constructed framework serves as a tool to investigate the existence of solutions for Caputo fractional differential equations, thereby highlighting both its effectiveness and practical significance.