Asymptotic properties of discrete linear fractional equations

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

Identyfikatory

DOI

10.24425/bpasts.2019.130184

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

linear discrete-time fractional systems; Caputo equation; Riemann-Liouville equation; Volterra convolution equation; stability

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2019
• Tom: Vol. 67, nr 4
• Strony: 749--759
• Opis fizyczny: Bibliogr. 40 poz.

Twórcy

autor

Anh P. T.

• Department of Mathematics, Le Quy Don Technical University, 236 Hoang Quoc Viet, Ha noi, Vietnam

autor

Babiarz A.

• Silesian University of Technology, Faculty of Automatic Control, Electronics and Computer Science, Akademicka 16, 44-100 Gliwice, Poland

autor

Czornik A.

• Silesian University of Technology, Faculty of Automatic Control, Electronics and Computer Science, Akademicka 16, 44-100 Gliwice, Poland

autor

Niezabitowski M.

• Silesian University of Technology, Faculty of Automatic Control, Electronics and Computer Science, Akademicka 16, 44-100 Gliwice, Poland
• University of Silesia, Faculty of Mathematics, Physics and Chemistry, Bankowa 14, 40-007 Katowice, Poland

autor

Siegmund S.

• Technische Universität Dresden, Faculty of Mathematics, Zellescher Weg 12-14, 01069 Dresden, Germany

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).