Generalized Hukuhara differentiability of interval-valued functions and interval differential equations

In the present paper we use a recently proposed generalization of the Hukuhara difference for compact convex sets, to introduce and study a generalization of the Hukuhara differentiability to the case of interval-valued functions. We also consider several possible definitions for the derivative of an interval-valued function, recently proposed in the literature, and we study connections between them and their properties. Using these concepts we study interval differential equations. Local existence and uniqueness of two solutions is obtained together with characterizations of the solutions of an interval differential equation by ODE systems. Several examples are also shown.