Relation-theoretic metrical fixed-point results via $$\varvec{w}$$ w -distance with applications

Abstract

In this article, utilizing the concept of w-distance, we prove the celebrated Banach’s fixed-point theorem in metric spaces equipped with an arbitrary binary relation. Necessarily, our findings unveil another direction of relation-theoretic metrical fixed-point theory. In addition, our paper consists of several non-trivial examples which signify the motivation of such investigations. Finally, our obtained results enable us to explore the existence of solutions of nonlinear fractional differential equations and fractional thermostat model involving the Caputo fractional derivative.