Detail publikace

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

ČERMÁK, J. NECHVÁTAL, L.

Anglický název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

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 anglicky

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

Vydáno

01.07.2020

Nakladatel

PERGAMON-ELSEVIER SCIENCE LTD

Místo

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

ISSN

0893-9659

Ročník

105

Číslo

1

Strany od–do

1–9

Počet stran

9

BIBTEX


@article{BUT162615,
  author="Jan {Čermák} and Luděk {Nechvátal},
  title="On exact and discretized stability of a linear fractional delay differential equation",
  year="2020",
  volume="105",
  number="1",
  month="July",
  pages="1--9",
  publisher="PERGAMON-ELSEVIER SCIENCE LTD",
  address="THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND",
  issn="0893-9659"
}