In this paper, we establish certain fixed point theorems for (φ, ψ, p)-weakly contractive mappings on relational metric spaces by using the notion of w-distance and locally S-transitivity of binary relation. Our results generalize the results of Alam and Imdad (J. many others of the existing literature. Moreover, we have an application to the nonlinear Fredholm integral equations and some illustrative examples to reveal the usability of our findings.