Fractional Dynamics and Fixed Point Theorems in Neutrosophic MR-Metric Spaces with Applications to Network Systems

Abstract

 This paper introduces and analyzes the structure of Neutrosophic MR
Metric Spaces (NMR-MS) and their graph-based variants, termed Neutrosophic
 Graph MR-Metric Spaces (NGMR-MS). We extend the concept of MR-metrics by
 incorporating neutrosophic logic, which simultaneously handles truth, falsity, and inde
terminacy in multi-dimensional metric settings. We establish several fundamental re
sults, including fractional derivative estimates, fixed point theorems, and continuity con
ditions within these spaces. Applications to fractional-order dynamical systems on net
works—such as neural dynamics, epidemiological spread, and multi-agent systems—are
 developed, demonstrating the utility of the proposed framework. Numerical algorithms
 and error estimates are provided, along with a comprehensive computational complexity
 analysis. The results generalize and unify several existing theories in fixed point theory,
 fractional calculus, and neutrosophic analysis.

DOI: 10.5281/zenodo.17102639