Enhancing Generalized Interpolative Contraction Through Simulation Functions

In the present manuscript, we elucidate a comprehensive framework for the generalized interpolative $\alpha-(\psi,\varphi)_Z-$contractive mapping, thereby extending the foundational theoretical constructs to augment its utility within the domain of advanced mathematical analysis. The investigation encompasses a meticulous examination of fixed point results within the context of non-Archimedean modular metric spaces, which are characterized by their distinctive structural properties that diverge from those of conventional metric spaces. Moreover, we apply the results attained to substantiate the existence and uniqueness of solutions pertaining to nonlinear Fredholm integral equations. This aspect of our inquiry underscores the practical implications of our theoretical advancements and provides a rigorous framework for the resolution of complex integral equations through the principles of established contractive mappings.