Publication result detail

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

KISELA, T.; ČERMÁK, J.

Original Title

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

English Title

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

Type

WoS Article

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.

English 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

Key words in English

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

Authors

KISELA, T.; ČERMÁK, J.

RIV year

2016

Released

30.04.2015

ISBN

1311-0454

Periodical

Fractional Calculus and Applied Analysis

Volume

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"
}