Hyers-Ulam stability of linear quaternion-valued differential equations

Abstract

In this article, we study the Hyers-Ulam stability of the first-order linear quaternion-valued differential equations. We transfer a linear quaternion-valued differential equation into a real differential system. The Hyers-Ulam stability results for the linear quaternion-valued differential equations are obtained according to the equivalent relationship between the vector 2-norm and the quaternion module.