New common fixed point theorems for quartet mappings on orthogonal S -metric spaces with applications

In this article, we extend the scope of fixed point theory by proving a common fixed point theorem applicable to quartet mappings defined on orthogonal \(\mathcal{S}\)-metric spaces. Our theorems establish conditions under which the quartet mappings \(\Phi, \Psi, \mathcal{H}\), and \(\mathcal{K}\) are orthogonal preserving, orthogonal continuous, and pairwise compatible mappings, possess a unique common fixed point. To elucidate the practical implications of our theoretical result, we present a concrete example illustrating its application. Finally, we demonstrate the versatility of our theorem by applying it to establish the existence and uniqueness of solutions for Volterra-type integral system, production-consumption equilibrium and fractional differential equations.