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1 Bulletin of the Polish Academy of Sciences. Technical Sciences

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Asymptotic properties of discrete linear fractional equations

Anh P. T., Babiarz A., Czornik A., Niezabitowski M., Siegmund S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 4

749--759

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.