In this paper, we provide the notion of a generalized neutrosophic contraction, which extends the concepts of neutrosophic non-expansive mappings and neutrosophic Banach contractions. Using this approach, we proved a fixed point theorem and demonstrated the existence and uniqueness of a solution in the context of neutrosophic metric space and discussed its importance with some appealing applications such as the satellite web coupling problem. We also investigated a new avenue in fractal function production, where fractal structures are constructed using neutrosophic Hutchinson-Barnsley (NHB) operators. We have provided a variety of very interesting examples to illustrate the efficiency of our work in complicated dynamical systems, fractal geometry, and iterated function systems (IFS). We set the stage for future studies in applied mathematics, stability analysis, and fixed point theory by utilizing neutrosophic contraction principles.