On explicit stability conditions for a linear fractional difference system

Jan Čermák, István Gyori, Luděk Nechvátal

Research output: Contribution to journalArticle

50 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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Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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