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In this article, utilizing the concept of w-distance, we prove the celebratedBanach's fixed point theorem in metric spaces equipped with an arbitrary binaryrelation. Necessarily our findings unveil another direction ofrelation-theoretic metrical fixed point theory. Also, our paper consists ofseveral non-trivial examples which signify the motivation for suchinvestigations. Finally, our obtained results enable us to explore theexistence and uniqueness of solutions of nonlinear fractional differentialequations involving the Caputo fractional derivative.

Relation-theoretic metrical fixed point results via w-distance with an application in nonlinear fractional differential equations