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.