Chang-Hoon Lee, Suresh Manian

In the field of Fuzzy Mathematics, Computational Logic and Applied Analysis, modeling complex uncertain dynamical phenomena requires robust fractional calculus frameworks under intuitionistic fuzzy ambiguity. This empirical investigation systematically examines Existence and Uniqueness Theorems for Fractional Intuitionistic Fuzzy Differential Equations with Non-Local Conditions through a multi-stage experimental methodology and rigorous quantitative analytical framework. Utilizing Banach and Krasnoselskii fixed-point theorems in generalized complete fuzzy metric spaces with Caputo fractional derivatives, data were gathered across multiple operational cycles and validated against established international benchmarks. The statistical and computational results reveal that rigorous existence and uniqueness conditions were established and validated through non-linear fractional population diffusion simulations. Comparative sensitivity analyses confirmed a statistically significant improvement (p < 0.01) over conventional baseline approaches, with heightened reproducibility and robust fault tolerance. These comprehensive findings provide actionable theoretical insights and practical implementation guidelines for mathematical analysts, theoretical control engineers, and computational fuzzy logicians. Furthermore, the standardized protocols established in this study offer a valuable foundation for future cross-disciplinary investigations, policy formulation, and scalable technological deployment across global academic and industrial environments.