Further new refinements in h-stability conditions for nonlinear abstract dynamic equations on time scales and applications

Abstract

In this paper, we study the h-stability problems of some classes of dynamic equations as an extension of exponential stability. We derive some sufficient conditions that guarantee h-stability of perturbed dynamic equations using Grönwall-Bihari and Pachpatte type integral inequality approch. Finally, numerical examples are introduced to illustrate the applicability of the main results.

Keywords

• abstract dynamic equation
• time scale
• integral inequality
• semi-group
• h-stability