Hyers–Ulam Stability of Linear Quaternion-Valued Differential Equations with Two-Sided Constant Coefficients

In this paper, the Hyers–Ulam stability of linear quaternion-valued differential equations with two-sided constant coefficients are studied. Utilizing the complex representation of quaternions, we transform a nth-order quaternion-valued differential equation with two-sided constant coefficients into four nth-order complex differential equations. Then we derive the Hyers–Ulam stability by means of the reduced order method and the relationship between the quaternion-valued differential equations and the system of complex-valued differential equations. Two examples are presented to illustrate the validity of the theoretical results.