Weak C-Contraction Mappings in S-Metric Spaces and Fixed Point Theorems

This study seeks to formulate and establish multiple fixed point and common fixed point theorems for a novel class of contractions, called C-type contractions, within the context of S-metric spaces. Furthermore, we provide illustrative examples to substantiate the theoretical findings. The results of this study generalize and extend several previous results in the literature. We use these fixed point results to establish the existence and uniqueness of solutions for a class of conformable differential equations, representing a recent development in fractional calculus.