A novel approach to Lyapunov eventual stability of Caputo fractional dynamic equations on time scale

Abstract

This paper introduces a novel approach to the Lyapunov eventual stability of Caputo fractional dynamic equations on time scales. By utilizing comparison principle, we develop eventual stability results that simultaneously holds for discrete and continuous domains allowing for an in-depth study of systems that exhibit both continuous and abrupt changes over time ensuring that the system behavior becomes stable after a finite time, which is particularly useful in scenarios involving transient disturbances. We also give an illustrative example to show the applicability of our method.