In this paper we study the dynamical behavior of linear discrete-time fractional systems. The first main result is that the norm of the difference of two different solutions of a time-varying discrete-time Caputo equation tends to zero not faster than polynomially. The second main result is a complete description of the decay to zero of the trajectories of one-dimensional time-invariant stable Caputo and Riemann-Liouville equations. Moreover, we present Volterra convolution equations, that are equivalent to Caputo and Riemann-Liouvile equations and we also show an explicit formula for the solution of systems of time-invariant Caputo equations.

JO - Bulletin of the Polish Academy of Sciences: Technical Sciences L1 - http://so.czasopisma.pan.pl/Content/113668/PDF/08_749-760_01073_Bpast.No.67-4_30.08.19_K1_TeX.pdf L2 - http://so.czasopisma.pan.pl/Content/113668 IS - No. 4 EP - 759 KW - linear discrete-time fractional systems KW - Caputo equation KW - Riemann-Liouville equation KW - Volterra convolution equation KW - stability ER - A1 - Anh, P.T. A1 - Babiarz, A. A1 - Czornik, A. A1 - Niezabitowski, M. A1 - Siegmund, S. VL - 67 JF - Bulletin of the Polish Academy of Sciences: Technical Sciences SP - 749 T1 - Asymptotic properties of discrete linear fractional equations UR - http://so.czasopisma.pan.pl/dlibra/docmetadata?id=113668 DOI - 10.24425/bpasts.2019.130184