Generalized Nonlinear Rational Contractions via Coupled Fixed Points Under a Binary Relation with Application to Fractional Differential Equations

Abstract

In this article, we use a binary relation to demonstrate the existence and uniqueness of fixed points and coupled fixed point results in the context of metric space under the new generalized (φ, ψ)-rational contraction. Moreover, we employed the mixed -monotone property of a mapping and utilize the same to investigate the existence and uniqueness of coupled fixed points endowed with a binary relation . Additionally, we present an example to demonstrate our recently validated findings. Lastly, we provide an application to fractional differential equation.