Boyd-Wong contractions in F-metric spaces and applications

Abstract

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.

Keywords

• $\mathcal{f}$-metric space
• fractional differential equation
• boyd-wong fixed point theorem