Existence of solutions to a class of interval-valued differential equation with impulses relative to length constraints

Abstract

This paper provides a new model framework to study interval-valued dynamical systems with length constraints. We use impulses instead of switching points to control the length of solutions to interval-valued differential equation under gH-differentiability. Firstly, we consider a class of interval-valued differential equation with impulses. Then, we study interval-valued differential equation with impulses relative to length constraints. Applying fixed point theory in metric space, we prove some existence results. Several examples are given to illustrate the theoretical results.