Detail publikačního výsledku

Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case

KISELA, T.; ČERMÁK, J.

Originální název

Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case

Anglický název

Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

fractional differential equation; fractional difference equation; asymptotic stability; fractional Schur-Cohn criterion

Klíčová slova v angličtině

fractional differential equation; fractional difference equation; asymptotic stability; fractional Schur-Cohn criterion

Autoři

KISELA, T.; ČERMÁK, J.

Rok RIV

2016

Vydáno

30.04.2015

ISSN

1311-0454

Periodikum

Fractional Calculus and Applied Analysis

Svazek

18

Číslo

2

Stát

Bulharská republika

Strany od

437

Strany do

458

Strany počet

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"
}