Generalized Hukuhara differentiability of interval-valued functions andinterval differential equations

摘要

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