New fixed point theorems in extended orthogonal S-metric spaces of type (µ,σ) with applications to fractional integral equations

In this article, we propose the concept of extended orthogonal S-metric spaces of type (m,s) and explore several related properties and theorems based on this concept. We provide examples to validate our findings. Finally, we illustrate the practical relevance of our results through applications to the fractional integral equations and Fredholm integral equation, highlighting the advantages of our findings.