Quaternion-Valued Linear Impulsive Differential Equations

Abstract

In this paper, we transfer the approach of finding the explicit solutions to linear impulsive differential equations (LIDEs) to quaternion-valued case. We develop the similar idea to find the solutions to LIDEs and give the details to derive the representations of the solutions to quaternion-valued LIDEs in the sense of complex numbers and quaternion. In addition, we present that two formulas are equivalent to each other. Finally, some examples are given to illustrate the theory approach.