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.

}, type={ArtykuĹ‚y / Articles}, title={Asymptotic properties of discrete linear fractional equations}, volume={67}, number={No. 4}, pages={749-759}, journal={Bulletin of the Polish Academy of Sciences: Technical Sciences}, doi={10.24425/bpasts.2019.130184}, keywords={linear discrete-time fractional systems, Caputo equation, Riemann-Liouville equation, Volterra convolution equation, stability}, }