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KISELA, T. ČERMÁK, J.
Original Title
Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case
Type
journal article in Web of Science
Language
English
Original Abstract
The paper discusses asymptotic stability conditions for the linear fractional difference equation ∇αy(n) + a∇βy(n) + by(n) = 0 with real coefficients a, b and real orders α > β > 0 such that α/β is a rational number. For given α, β, we describe various types of discrete stability regions in the (a, b)-plane and compare them with the stability regions recently derived for the underlying continuous pattern Dαx(t) + aDβx(t) + bx(t) = 0 involving two Caputo fractional derivatives. Our analysis shows that discrete stability sets are larger and their structure much more rich than in the case of the continuous counterparts.
Keywords
fractional differential equation; fractional difference equation; asymptotic stability; fractional Schur-Cohn criterion
Authors
KISELA, T.; ČERMÁK, J.
RIV year
2015
Released
30. 4. 2015
ISBN
1311-0454
Periodical
Fractional Calculus and Applied Analysis
Year of study
18
Number
2
State
Republic of Bulgaria
Pages from
437
Pages to
458
Pages count
22
BibTex
@article{BUT115854, author="Tomáš {Kisela} and Jan {Čermák}", title="Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case", journal="Fractional Calculus and Applied Analysis", year="2015", volume="18", number="2", pages="437--458", doi="10.1515/fca-2015-0028", issn="1311-0454" }