Toward stability investigation of fractional dynamical systems on time scale

Abstract

We study dynamic systems on time scales that are generalizations of classical differential or difference equations. In this paper, we present the asymptotic stability of linear fractional time-invariant systems with the Caputo ∆−derivative on time scale. To ensure the asymptotic stability of this kind of system, some results about necessary and sufficient conditions are investigated, resulting in a region of asymptotic stability. Furthermore, we obtain the results of the asymptotic stability by transforming the stability region of the continuous-time case through suitable M¨obious transformations.