Relation-Theoretic Banach Contraction Principle in Topological Spaces with an Application

Abstract: In this article, we extend several relation-theoretic notions to topological spaces. We introduce relation preserving contraction mapping into topological spaces and utilize the same to extend Banach contraction principle in topological spaces employing a binary relation. To illustrate the validity of our main result, we provide a concrete example along with a MATLAB-based visualization of the convergence behavior. Furthermore, we demonstrated the applicability of our main result by finding a solution for a fractional differential equation under some suitable assumptions.