Fixed point theorems under ω-distance functions and applications to nonlinear integral and fractional differential equations

Abstract

In this paper, we utilize the family F and the notion of ω-distance in an ordered G-metric space and introduce (F, ω)-contractions in order to derive some fixed point results. We also discuss the problems of Ulam-Hyers stability, well-posedness and limit shadowing property. In order to illustrate the use of our results, we apply them to nonlinear integral equations, as well as to some three-point fractional integral boundary value problems, both with numerical examples.