New fixed point theorems in orthogonal -multiplicative metric spaces and applications to multiplicative and fractional integral equations

This paper explores fixed point theorems in the context of orthogonal (Formula presented.) -multiplicative metric spaces, which extend traditional metric spaces by incorporating both orthogonality and multiplicative structures. To demonstrate the novelty and practical relevance of our main results, we include examples and applications to multiplicative integral equations and Riemann–Liouville fractional integral equations.