Integral-type contraction, S $\mathcal{S}$ -metric spaces, Orthogonal metric spaces, Riemann–Liouville fractional integral, Applied mathematics. Quantitative methods, T57-57.97, Analysis, QA299.6-433

Abstract In this article, we present common fixed-point theorems for contractions of integral type within the framework of orthogonal S $\mathcal{S}$ -metric spaces. Examples are provided to illustrate the findings. This work extends and generalizes numerous results from existing literature. Furthermore, the theoretical results are reinforced through an application to a fractional integral equation.