Publication details

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

Authors

DOŠLÁ Zuzana ČERMÁK Jan KISELA Tomáš

Year of publication 2017
Type Article in Periodical
Magazine / Source Applied Mathematics and Computation
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1016/j.amc.2016.11.016
Keywords Delay differential equation; fractional-order derivative; stability; asymptotic behavior
Description 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.