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Asymptotic properties of discrete linear fractional equations

Anh, P.T. and Babiarz, A. and Czornik, A. and Niezabitowski, M. and Siegmund, S. (2019) Asymptotic properties of discrete linear fractional equations. Bulletin of the Polish Academy of Sciences: Technical Sciences, 67 (4). pp. 749-759. ISSN 2397528

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Abstract

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 C'aputo 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 C'aputo 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. © 2019 Polish Academy of Sciences. All rights reserved.

Item Type: Article
Divisions: Faculties > Faculty of Information Technology
Identification Number: 10.24425/bpasts.2019.130184
Uncontrolled Keywords: Convergence of numerical methods; Convolution; Asymptotic properties; Caputo equation; Convolution equations; Dynamical behaviors; Explicit formula; Fractional equation; Fractional systems; Time invariants; Liouville equation
Additional Information: Language of original document: English.
URI: http://eprints.lqdtu.edu.vn/id/eprint/9434

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