Detail publikačního výsledku

On exact and discretized stability of a linear fractional delay differential equation

ČERMÁK, J.; NECHVÁTAL, L.

Originální název

On exact and discretized stability of a linear fractional delay differential equation

Anglický název

On exact and discretized stability of a linear fractional delay differential equation

Druh

Článek WoS

Originální abstrakt

The paper discusses the problem of necessary and sufficient stability conditions for a test fractional delay differential equation and its discretization. First, we recall the existing condition for asymptotic stability of the exact equation and consider an appropriate fractional delay difference equation as its discrete counterpart. Then, using the Laplace transform method combined with the boundary locus technique, we derive asymptotic stability conditions in the discrete case as well. Since the studied fractional delay difference equation serves as a backward Euler discretization of the underlying differential equation, we discuss a related problem of numerical stability (with a negative conclusion). Also, as a by-product of our observations, a fractional analogue of the classical Levin–May stability condition is presented.

Anglický abstrakt

The paper discusses the problem of necessary and sufficient stability conditions for a test fractional delay differential equation and its discretization. First, we recall the existing condition for asymptotic stability of the exact equation and consider an appropriate fractional delay difference equation as its discrete counterpart. Then, using the Laplace transform method combined with the boundary locus technique, we derive asymptotic stability conditions in the discrete case as well. Since the studied fractional delay difference equation serves as a backward Euler discretization of the underlying differential equation, we discuss a related problem of numerical stability (with a negative conclusion). Also, as a by-product of our observations, a fractional analogue of the classical Levin–May stability condition is presented.

Klíčová slova

Fractional delay differential and difference equation; Asymptotic stability; Numerical stability

Klíčová slova v angličtině

Fractional delay differential and difference equation; Asymptotic stability; Numerical stability

Autoři

ČERMÁK, J.; NECHVÁTAL, L.

Rok RIV

2021

Vydáno

01.07.2020

Nakladatel

PERGAMON-ELSEVIER SCIENCE LTD

Místo

THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND

ISSN

0893-9659

Periodikum

Applied Mathematics Letters

Svazek

105

Číslo

1

Stát

Spojené státy americké

Strany od

1

Strany do

9

Strany počet

9

URL

https://www.sciencedirect.com/science/article/pii/S0893965920300896

BibTex

@article{BUT162615,
  author="Jan {Čermák} and Luděk {Nechvátal}",
  title="On exact and discretized stability of a linear fractional delay differential equation",
  journal="Applied Mathematics Letters",
  year="2020",
  volume="105",
  number="1",
  pages="1--9",
  doi="10.1016/j.aml.2020.106296",
  issn="0893-9659",
  url="https://www.sciencedirect.com/science/article/pii/S0893965920300896"
}