Differentiability Structure of Solutions to Fuzzy Differential Equations under the Generalized Derivative

This work intends to disseminate the results obtained in Longo et al (2026) concerning the application of the Hukuhara-type derivatives to fuzzy differential equations. The generalized derivative represents the broadest notion of the Hukuhara-type derivative of a fuzzy number-valued function in the literature. It exists for a wide class of fuzzy processes, since the generalized difference exists for any pair of fuzzy numbers. Despite its historical significance, few papers provide theoretical results on the g-derivative, primarily because of its complex analytical behavior. On the other hand, analyzing solutions to fuzzy differential equations from a comparative Hukuhara-type perspective allows establishing features of FDEs whose solutions are exclusively g-differentiable. The work starts by presenting the results and examples from Longo et al (2026) and, after that, establishes a generalized version of the main theorem for systems of fuzzy differential equations.