Quaternion-Valued Dynamic Equations and Henstock–Kurzweil Delta-Integrals on Time Scales: A Survey

Quaternionic calculus is significant in applied mathematics. It is closely referred to mathematical physics and engineering sciences. Our aim is to present some advances in the investigations of the quaternion dynamic equations on time scales and the Henstock–Kurzweil ∆-integral (abbreviated as HK-∆-integral) and to introduce the corresponding quaternionic version of the HK-∆-integral (abbreviated as HK^Q-∆-integral). Some basic properties of the HK^Q-∆-integral are demonstrated, which would be helpful in the future research in this direction.