New fixed point theorems with applications to non-linear neutral differential equations

Abstract

The aim of this study is to investigate the existence of solutions for a non-linear neutral differential equation with an unbounded delay. To achieve our goals, we take advantage of fixed point theorems for self-mappings satisfying a generalized (α, ϕ) rational contraction, as well as cyclic contractions in the context of F-metric spaces. We also supply an example to support the new theorem.