On explicit stability conditions for a linear fractional difference system

• Published in: Fractional calculus & applied analysis Vol. 18; no. 3; pp. 651 - 672
• Main Authors: Čermák, Jan, Győri, István, Nechvátal, Ludĕk
• Format: Journal Article
• Language: English
• Published: Warsaw Versita 01.06.2015; De Gruyter Open; Nature Publishing Group
• Subjects: Abstract Harmonic Analysis; Analysis; asymptotic stability; Caputo difference operator; fractional-order difference system; Functional Analysis; Integral Transforms; Mathematics; Operational Calculus; Research Paper; Riemann-Liouville difference operator; Caputo difference operator; Riemann-Liouville difference operator; Primary 26A33; Secondary 34A08, 39A12, 39A30; asymptotic stability; fractional-order difference system
• ISSN: 1311-0454; 1314-2224
• DOI: 10.1515/fca-2015-0040

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.