Hybrid Soft-Neutrosophic Controlled Metric Spaces with Applications to Nonlinear Chemical Reaction Networks

Abstract

In this paper, we introduce a novel mathematical framework called Hybrid Soft-Neutrosophic Controlled Metric Space (HSNCMS), which integrates soft set theory, neutrosophic sets, and controlled metric spaces. We develop auxiliary lemmas and establish a Banach-type fixed point theorem with complete proof for HSNCMS and introduce the concept of T-controlled contraction with related results. Furthermore, as an application we prove the existence and uniqueness of equilibrium concentration profiles for a nonlinear chemical reaction network, where uncertainty arises from fluctuations in temperature, pressure, catalyst effects, and incomplete experimental data. The proposed model generalizes several existing structures and provides a flexible tool for handling uncertainty, indeterminacy, and parameterization simultaneously.