On Some Properties of Linear Systems on Time Scales With Tractability Index Greater Than One
Abstract
The linear non-homogeneous systems of difference equations on time scales with delta derivatives are studied. We introduce a class of linear time-varying dynamic-algebraic equations(LTVDAE) of tractability index $\geq 2$ on arbitrary time scales. We propose a procedure for the decoupling of the considered class of linear time-varying dynamic-algebraic equations. The methods of the paper are constructive: we use the projector approach where the tractability index is just the number of necessary projector. Moreover, we give conditions on coefficients of our system which guarantee the existence of the chain of projectors and makes decoupling possible. This work is a continuation (and a more sophisticated case) of our previous article \cite{SGSK1} where we study equations of index 1. The obtained results may be applied in various areas of time scale dynamics, for example, in Stability Theory.
Keywords
Thanks
The work of the second co-author was supported by Gdansk University of Technology by the DEC 14/2021/IDUB/I.1 grant under the Nobelium - 'Excellence Initiative - Research University' program.
References
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Details
Primary Language
English
Subjects
Ordinary Differential Equations, Difference Equations and Dynamical Systems
Journal Section
Research Article
Publication Date
March 30, 2026
Submission Date
October 3, 2025
Acceptance Date
January 9, 2026
Published in Issue
Year 1970 Volume: 9 Number: 1
APA
Georgiev, S., & Kryzhevich, S. (2026). On Some Properties of Linear Systems on Time Scales With Tractability Index Greater Than One. Fundamental Journal of Mathematics and Applications, 9(1), 1-22. https://doi.org/10.33401/fujma.1796460
AMA
1.Georgiev S, Kryzhevich S. On Some Properties of Linear Systems on Time Scales With Tractability Index Greater Than One. Fundam. J. Math. Appl. 2026;9(1):1-22. doi:10.33401/fujma.1796460
Chicago
Georgiev, Svetlin, and Sergey Kryzhevich. 2026. “On Some Properties of Linear Systems on Time Scales With Tractability Index Greater Than One”. Fundamental Journal of Mathematics and Applications 9 (1): 1-22. https://doi.org/10.33401/fujma.1796460.
EndNote
Georgiev S, Kryzhevich S (March 1, 2026) On Some Properties of Linear Systems on Time Scales With Tractability Index Greater Than One. Fundamental Journal of Mathematics and Applications 9 1 1–22.
IEEE
[1]S. Georgiev and S. Kryzhevich, “On Some Properties of Linear Systems on Time Scales With Tractability Index Greater Than One”, Fundam. J. Math. Appl., vol. 9, no. 1, pp. 1–22, Mar. 2026, doi: 10.33401/fujma.1796460.
ISNAD
Georgiev, Svetlin - Kryzhevich, Sergey. “On Some Properties of Linear Systems on Time Scales With Tractability Index Greater Than One”. Fundamental Journal of Mathematics and Applications 9/1 (March 1, 2026): 1-22. https://doi.org/10.33401/fujma.1796460.
JAMA
1.Georgiev S, Kryzhevich S. On Some Properties of Linear Systems on Time Scales With Tractability Index Greater Than One. Fundam. J. Math. Appl. 2026;9:1–22.
MLA
Georgiev, Svetlin, and Sergey Kryzhevich. “On Some Properties of Linear Systems on Time Scales With Tractability Index Greater Than One”. Fundamental Journal of Mathematics and Applications, vol. 9, no. 1, Mar. 2026, pp. 1-22, doi:10.33401/fujma.1796460.
Vancouver
1.Svetlin Georgiev, Sergey Kryzhevich. On Some Properties of Linear Systems on Time Scales With Tractability Index Greater Than One. Fundam. J. Math. Appl. 2026 Mar. 1;9(1):1-22. doi:10.33401/fujma.1796460
