On explicit stability conditions for a linear fractional difference system

Jan Čermák, I. Győri, Luděk Nechvátal

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

The paper describes the stability area for the difference system (Δαy)(n + 1 - α) = Ay(n), n= 0, 1., with the Caputo forward difference operator Δα of a real order α ∈ (0, 1) and a real constant matrix A. Contrary to the existing result on this topic, our stability conditions are fully explicit and involve the decay rate of the solutions. Some comparisons with a difference system of the Riemann- Liouville type are discussed as well, including related consequences and illustrating examples.

Original languageEnglish
Pages (from-to)651-672
Number of pages22
JournalFractional Calculus and Applied Analysis
Volume18
Issue number3
DOIs
Publication statusPublished - Jun 1 2015

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Stability Condition
Fractional
Difference Operator
Decay Rate

Keywords

  • asymptotic stability
  • Caputo difference operator
  • fractional-order difference system
  • Riemann-Liouville difference operator

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

On explicit stability conditions for a linear fractional difference system. / Čermák, Jan; Győri, I.; Nechvátal, Luděk.

In: Fractional Calculus and Applied Analysis, Vol. 18, No. 3, 01.06.2015, p. 651-672.

Research output: Contribution to journalArticle

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