Fixed-Point Results of Generalized (ϕ,Ψ)-Contractive Mappings in Partially Ordered Controlled Metric Spaces with an Application to a System of Integral Equations

In this manuscript, we prove numerous results concerning fixed points, common fixed points, coincidence points, coupled coincidence points, and coupled common fixed points for $(\varphi ,\Psi )$-contractive mappings in the framework of partially ordered controlled metric spaces. Our findings introduce a novel perspective on this mathematical context, and we illustrate the uniqueness of our findings through various explanatory examples. Also, we apply the main result to find the existence and uniqueness of the solution of the system of integral equations as an application.