Approaching fractals in complete neutrosophic metric spaces via best proximity points

Abstract In this research article, motivated by the strong connection between fixed point theory and fractal theory, we present an innovative method to the study of fractals in the context of neutrosophic metric spaces through the best proximity points. We introduce the concept of neutrosophic proximal iterated function systems generated by a finite collection of proximal contractions in neutrosophic metric spaces, which expands the idea of iterated function systems, one of the most widely used methods for creating fractals. As a new method for creating fractals, we thus suggest a result showing that the neutrosophic proximal iterated function system has a unique best attractor under certain conditions on neutrosophic metric spaces. We illustrate our conclusions with examples.