On the semigroup approach to the interval-valued differential evolution equations

Abstract

In this paper, we introduce the semigroups of semilinear mappings on the space of nonempty compact intervals of $${\mathbb {R}}$$ . Some important properties of strongly continuous semigroups of interval-valued mappings are investigated. Depending on the different types of generalized Hukuhara differences, the interval-valued infinitesimal generators and resolvent operators are defined and the Hille–Yosida like representation of resolvent operators is given. As an application, the unique existence of mild solutions for Cauchy problems of interval-valued evolution equations is given.