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 and Tomáš KISELA

Basic information

Original name

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

Authors

DOŠLÁ, Zuzana (203 Czech Republic, belonging to the institution), Jan ČERMÁK (203 Czech Republic) and Tomáš KISELA (203 Czech Republic)

Edition

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

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 2.300

RIV identification code

RIV/00216224:14310/17:00100417

Organization unit

Faculty of Science

DOI

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

UT WoS

000392785400026

Keywords in English

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

Abstract

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 and Tomáš KISELA. Fractional differential equations with a constant delay: statiblity and asymptotics of solutions. Applied Mathematics and Computation. New York: ELSEVIER SCIENCE INC, 2017, vol. 298, April, p. 336-350. ISSN 0096-3003. Available from: 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 and 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, vol.~298, April, p.~336-350. ISSN~0096-3003. Available from: https://dx.doi.org/10.1016/j.amc.2016.11.016.

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