Fractional differential equations with a constant delay:
statiblity and asymptotics of solutions

J 2017

Fractional differential equations with a constant delay: statiblity and asymptotics of solutions

DOŠLÁ, Zuzana, Jan ČERMÁK a Tomáš KISELA

Základní údaje

Originální název

Fractional differential equations with a constant delay: statiblity and asymptotics of solutions

Autoři

DOŠLÁ, Zuzana (203 Česká republika, domácí), Jan ČERMÁK (203 Česká republika) a Tomáš KISELA (203 Česká republika)

Vydání

Applied Mathematics and Computation, New York, ELSEVIER SCIENCE INC, 2017, 0096-3003

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 2.300

Kód RIV

RIV/00216224:14310/17:00100417

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1016/j.amc.2016.11.016

UT WoS

000392785400026

Klíčová slova anglicky

Delay differential equation; fractional-order derivative; stability; asymptotic behavior

Štítky

NZ, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 4. 4. 2018 08:54, Ing. Nicole Zrilić

Anotace

V originále

The paper discusses the stability and asymptotic behavior of fractional-order differential equations involving both delayed as well as nondelayed terms. As the main results, the necessary and sufficient conditions guaranteeing asymptotic stability of its zero solution are presented, including asymptotic formulae for all its solutions. Since this equation represents a basic test equation for numerical analysis of delay differential equations of fractional type, the knowledge of its optimal stability conditions is crucial for investigations of numerical stability. Theoretical conclusions are supported by comments and comparisons distinguishing behaviour of a fractional-order delay equation from its integer-order pattern.

Citovat

DOŠLÁ, Zuzana, Jan ČERMÁK a Tomáš KISELA. Fractional differential equations with a constant delay: statiblity and asymptotics of solutions. Applied Mathematics and Computation. New York: ELSEVIER SCIENCE INC, 2017, roč. 298, April, s. 336-350. ISSN 0096-3003. Dostupné z: https://dx.doi.org/10.1016/j.amc.2016.11.016.

@article{1411792,
   author = {Došlá, Zuzana and Čermák, Jan and Kisela, Tomáš},
   article_location = {New York},
   article_number = {April},
   doi = {http://dx.doi.org/10.1016/j.amc.2016.11.016},
   keywords = {Delay differential equation; fractional-order derivative; stability; asymptotic behavior},
   language = {eng},
   issn = {0096-3003},
   journal = {Applied Mathematics and Computation},
   title = {Fractional differential equations with a constant delay: statiblity and asymptotics of solutions},
   volume = {298},
   year = {2017}
}

TY  - JOUR
ID  - 1411792
AU  - Došlá, Zuzana - Čermák, Jan - Kisela, Tomáš
PY  - 2017
TI  - Fractional differential equations with a constant delay: statiblity and asymptotics of solutions
JF  - Applied Mathematics and Computation
VL  - 298
IS  - April
SP  - 336-350
EP  - 336-350
PB  - ELSEVIER SCIENCE INC
SN  - 00963003
KW  - Delay differential equation
KW  - fractional-order derivative
KW  - stability
KW  - asymptotic behavior
N2  - The paper discusses the stability and asymptotic behavior of fractional-order differential equations involving both delayed as well as nondelayed terms. As the main results, the necessary and sufficient conditions guaranteeing asymptotic stability of its zero solution are presented, including asymptotic formulae for all its solutions. Since this equation represents a basic test equation for numerical analysis of delay differential equations of fractional type, the knowledge of its optimal stability conditions is crucial for investigations of numerical stability. Theoretical conclusions are supported by comments and comparisons distinguishing behaviour of a fractional-order delay equation from its integer-order pattern.
ER  -

DOŠLÁ, Zuzana, Jan ČERMÁK a Tomáš KISELA. Fractional differential equations with a constant delay: statiblity and asymptotics of solutions. \textit{Applied Mathematics and Computation}. New York: ELSEVIER SCIENCE INC, 2017, roč.~298, April, s.~336-350. ISSN~0096-3003. Dostupné z: https://dx.doi.org/10.1016/j.amc.2016.11.016.

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