𝒉�- Stability of Functional Dynamic Equations on Time Scales by Alternative Variation of Parameters

Abstract

In this paper, we concentrate on nonlinear functional dynamic equations of the form 𝒙�∆(𝒕�) = 𝒂�(𝒕�)𝒙�(𝒕�) +𝒇�(𝒕�,𝒙�(𝒕�)), 𝒕� ∈ 𝕋� on time scales and study ℎ-stability, which implies uniform exponential stability, uniform Lipschitz stability, or uniform stability in particular cases. In our analysis, we use an alternative variation of parameters, which enables us to focus on a larger class of equations since the dynamic equations under the spotlight are not necessarily regressive. Also, we establish a linkage between uniform boundedness and ℎ-stability notions for solutions of dynamic equations under sufficient conditions in addition to our stability results.