Asymptotic stability of the complex dynamic equation uΔ−z⋅u+w⋅uσ=0uΔ−z⋅u+w⋅uσ=0

In this paper, we provide sharp conditions for the complex time scale exponential function tend to zero asymptotically. More precisely, we study the asymptotic stability of the unique complex solution u=ez⊖μw(⋅,s)u=ez⊖μw(⋅,s) of the initial value problem{uΔ−z⋅u+w⋅uσ=0fort∈Tu(s)=1, where TT is a time scale with sup⁡T=∞sup⁡T=∞, s∈Ts∈T, and z,wz,w are complex constants. We also present an illustrative example to mention the sharpness of the main result.