Publication detail

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

ČERMÁK, J. NECHVÁTAL, L.

Original Title

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

English Title

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

Type

journal article in Web of Science

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

Released

01.07.2020

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

Location

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

Pages from

1

Pages to

9

Pages count

9

URL

Documents

BibTex


@article{BUT162615,
  author="Jan {Čermák} and Luděk {Nechvátal}",
  title="On exact and discretized stability of a linear fractional delay differential equation",
  annote="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.",
  address="PERGAMON-ELSEVIER SCIENCE LTD",
  chapter="162615",
  doi="10.1016/j.aml.2020.106296",
  howpublished="print",
  institution="PERGAMON-ELSEVIER SCIENCE LTD",
  number="1",
  volume="105",
  year="2020",
  month="july",
  pages="1--9",
  publisher="PERGAMON-ELSEVIER SCIENCE LTD",
  type="journal article in Web of Science"
}