In this chapter, we study coincidence point results via non-linear contraction on the settings of metric spaces endowed with relational structure. We supply two illustrative examples to reassert the claims of such novel findings. In addition, we also present some applications for the utility of such newly obtained results by solving fractional differential equations and Fredholm integral equations. These findings produce yet more analogous coincidence point results with some interesting applications. Thus, the aim is to substantiate the utility of such exploration by establishing some new core theoretical results with some interesting applications and important remarks on this theme.