Publication detail

The Lambert function method in qualitative analysis of fractional delay differential equations

ČERMÁK, J. KISELA, T. NECHVÁTAL, L.

English title

The Lambert function method in qualitative analysis of fractional delay differential equations

Type

journal article in Web of Science

Language

en

Original abstract

We discuss an analytical method for qualitative investigations of linear fractional delay differential equations. This method originates from the Lambert function technique that is traditionally used in stability analysis of ordinary delay differential equations. Contrary to the existing results based on such a technique, we show that the method can result into fully explicit stability criteria for a linear fractional delay differential equation, supported by a precise description of its asymptotics. As a by-product of our investigations, we also state alternate proofs of some classical assertions that are given in a more lucid form compared to the existing proofs.

English abstract

We discuss an analytical method for qualitative investigations of linear fractional delay differential equations. This method originates from the Lambert function technique that is traditionally used in stability analysis of ordinary delay differential equations. Contrary to the existing results based on such a technique, we show that the method can result into fully explicit stability criteria for a linear fractional delay differential equation, supported by a precise description of its asymptotics. As a by-product of our investigations, we also state alternate proofs of some classical assertions that are given in a more lucid form compared to the existing proofs.

Keywords in English

Fractional delay differential equation (primary); Lambert function; Stability; Asymptotic behavior

Released

16.06.2023

Publisher

Springer Nature

Location

CAMPUS, 4 CRINAN ST, LONDON N1 9XW, ENGLAND

ISSN

1311-0454

Volume

26

Number

4

Pages from–to

1545–1565

Pages count

21

BIBTEX


@article{BUT184060,
  author="Jan {Čermák} and Tomáš {Kisela} and Luděk {Nechvátal},
  title="The Lambert function method in qualitative analysis of fractional delay differential equations",
  year="2023",
  volume="26",
  number="4",
  month="June",
  pages="1545--1565",
  publisher="Springer Nature",
  address="CAMPUS, 4 CRINAN ST, LONDON N1 9XW, ENGLAND",
  issn="1311-0454"
}