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In this paper, we introduce the notion of fuzzy (F, φ,β-ψ)-contractive mappings in fuzzy metric spaces and utilize the same to prove some existence and uniqueness fuzzy φ-fixed point results in both M-complete and G-complete fuzzy metric spaces. The obtained results extend, generalize and improve some relevant results of the existing literature. An illustrative example is utilized to demonstrate the usefulness and effectiveness of our results. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study the Boyd-Wong type fixed point result in the F-metric context and apply it to obtain some existence and uniqueness criteria of solution(s) to a second order initial value problem and a Caputo fractional differential equation. We substantiate our obtained result by finding a suitable non-trivial example. [ABSTRACT FROM AUTHOR]