GENERALIZED HUKUHARA FRACTAL DIFFERENTIABILITY IN FUZZY MODELING

Abstract

This study introduces the concept of generalized Hukuhara fractal differentiability for fuzzy-valued functions and explores the necessary conditions for differentiability. The Atangana-Baleanu-Caputo fuzzy fractal-fractional derivative is developed, along with the corresponding integral operators. Theorems on existence and uniqueness of solutions are established, and a computational scheme is proposed for numerically solving fuzzy fractal-fractional differential equations. The effectiveness of the proposed method is demonstrated through the exponential population growth model, with numerical solutions compared against actual data using Mean Absolute Percentage Error. Comparative results highlight the improved accuracy of the fuzzy fractal-fractional approach over classical ordinary differential equations and fractional differential models. The proposed framework supports integration with machine learning by capturing memory, non-locality, and structural complexity, enabling advanced feature extraction, compact data representation, and improved model interpretability.