Abstract
The purpose of this paper is to define generalized (alpha beta-psi)-contraction in the context of F-metric space and obtain some new fixed point results. As applications, we solve a nonlinear neutral differential equation with an unbounded delay theta/(iota)=-rho 1(iota)theta(iota)+rho 2(iota)L(theta(iota-sigma(iota)))+rho 3(iota)theta/(iota-sigma(iota)), where rho 1(iota), rho 2(iota) are continuous, rho 3(iota) is continuously differentiable and sigma(iota)>0, for all iota is an element of R and is twice continuously differentiable.