Stability analysis of linear quaternion-valued differential equation using integral transform

In this article, we examine the stability of first-order linear quaternion-valued differential equations using the Mittag-Leffler-Hyers-Ulam approach. We achieve this by transforming a linear quaternion-valued differential equation into a real differential system. The stability outcomes for these linear quaternion-valued differential equations are determined through the use of quaternion module and Fourier transform techniques.