TOWARD STABILITY INVESTIGATION OF FRACTIONAL DYNAMICAL SYSTEMS ON TIME SCALE

TOWARD STABILITY INVESTIGATION OF FRACTIONAL DYNAMICAL SYSTEMS ON TIME SCALE

N. K. Mahdi, A. R. Khudair

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Abstract

We study dynamic systems on time scales that are generalizations of classical di erential or di erence 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 su cient 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 Mobious transformations.

Keywords

Time scale calculus; Linear dynamical systems; Fractional calculus; Stability.