Integral-type contraction on orthogonal $\mathcal{S}$-metric spaces with common fixed-point results and applications to fractional integral equations

Abstract In this article, we present common fixed-point theorems for contractions of integral type within the framework of orthogonal $\mathcal{S}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> </mml:math> -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.