This study introduces generalized contraction mappings in the context of \( S \) -metric spaces. We propose new types of contractions, namely \((\alpha _s, \psi , \varphi )\) - \(\textbf{D}\) , \((\alpha _s, \psi , \varphi )\) - \(\textbf{D}^{*}\) , and \((\alpha _s, \psi , \varphi )\) - \(\textbf{D}^{**}\) , which expand the existing notion of contractions in \( S \) -metric spaces. We prove fixed point theorems related to these contractions and provide concrete examples to validate the theoretical results. Additionally, we apply our findings to establish the existence of solutions to a second-order boundary value problem, showcasing the practical relevance of the proposed contractions.
