New fixed point results in orthogonal metric spaces with an application

Abstract

In this manuscript, owing to the concept of w-distance, we prove the much acclaimed Banach's fixed point theorem in orthogonal metric spaces. Further, our paper includes a couple of illustrative examples which exhibit the purpose for such inquests. In fact, the obtained results extend and improve certain comparable results of existing literature. Eventually, our findings allow us to obtain the existence and uniqueness of solutions of nonlinear fractional differential equations associated with the Caputo fractional derivative. Definition 1.1. Let X be a non-empty set and ⊥ be a binary relation defined on X × X. Then (X, ⊥) is said to be an orthogonal set (O-set) if there exists x 0 ∈ X

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