Relation-Theoretic Coupled Coincidence Fixed Point Results for Rational Type Contraction Mapping with Application to Fractional Boundary Value Problems

In this article, we establish the existence and uniqueness of coupled coincidence fixed points for rational-type contraction mappings in the framework of metric spaces by employing a binary relation. These results are derived under the assumption of the mixed monotone property. To illustrate the effectiveness of the obtained results, a suitable example is provided. Finally, we give an application of our main results to a fractional differential equation involving the Riemann–Liouville fractional derivatives. These findings extend existing results in the literature and highlight the effectiveness of the proposed approach in the analysis of fractional differential equations.