Asian Journal of Fuzzy and Applied Mathematics

Published by Asian Online Journals (AOJ) • ISSN (Online): 2321-564X • ISSN (Print): 2321-564X
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Existence and Uniqueness Theorems for Fractional Intuitionistic Fuzzy Differential Equations with Non-Local Conditions

Chang-Hoon Lee *
Suresh Manian *
* Pusan National University (Republic of Korea)
* University of Hyderabad (India)

Abstract

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.

Keywords

Intuitionistic Fuzzy Differential Equations Fractional Calculus Models Fixed-Point Mathematical Theorems Caputo Fractional Derivatives Generalized Fuzzy Metric Spaces Dynamical System Uncertainty
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Declarations & Ethics

Funding: Supported by the National Scientific Research Council & International Innovation Grants.
Conflicts of Interest: The authors declare no competing financial or institutional interests.
Peer Review: Double-blind peer reviewed by international subject specialists.
License: Creative Commons Attribution 4.0 International (CC BY 4.0).
How to Cite This Article
APA / MLA / BibTeX
Lee, et al. (2021). Existence and Uniqueness Theorems for Fractional Intuitionistic Fuzzy Differential Equations with Non-Local Conditions. Asian Journal of Fuzzy and Applied Mathematics, 9(1). https://doi.org/10.24203/ajfam.v9i1.7111
Lee, et al. "Existence and Uniqueness Theorems for Fractional Intuitionistic Fuzzy Differential Equations with Non-Local Conditions." Asian Journal of Fuzzy and Applied Mathematics, vol. 9, no. 1, 2021. https://doi.org/10.24203/ajfam.v9i1.7111
Lee, et al. "Existence and Uniqueness Theorems for Fractional Intuitionistic Fuzzy Differential Equations with Non-Local Conditions." Asian Journal of Fuzzy and Applied Mathematics 9, no. 1 (2021). https://doi.org/10.24203/ajfam.v9i1.7111