Detail publikačního výsledku

Stability properties of two-term fractional differential equations

KISELA, T.; ČERMÁK, J.

Originální název

Stability properties of two-term fractional differential equations

Anglický název

Stability properties of two-term fractional differential equations

Druh

Článek WoS

Originální abstrakt

This paper formulates explicit necessary and sufficient conditions for the local asymptotic stability of equilibrium points of the fractional differential equation Dα y(t) + f (y(t), Dβ y(t)) = 0, t > 0 involving two Caputo derivatives of real orders α>β such that α/β is a rational number. First, we consider this equation in the linearized form and derive optimal stability conditions in terms of its coefficients and orders α, β. As a byproduct, a special fractional version of the Routh–Hurwitz criterion is established. Then, using the recent developments on linearization methods in fractional dynamical systems, we extend these results to the original nonlinear equation. Some illustrating examples, involving significant linear and nonlinear fractional differential equations, support these results.

Anglický abstrakt

This paper formulates explicit necessary and sufficient conditions for the local asymptotic stability of equilibrium points of the fractional differential equation Dα y(t) + f (y(t), Dβ y(t)) = 0, t > 0 involving two Caputo derivatives of real orders α>β such that α/β is a rational number. First, we consider this equation in the linearized form and derive optimal stability conditions in terms of its coefficients and orders α, β. As a byproduct, a special fractional version of the Routh–Hurwitz criterion is established. Then, using the recent developments on linearization methods in fractional dynamical systems, we extend these results to the original nonlinear equation. Some illustrating examples, involving significant linear and nonlinear fractional differential equations, support these results.

Klíčová slova

Fractional differential equation; Caputo derivative; Asymptotic stability; Equilibrium point

Klíčová slova v angličtině

Fractional differential equation; Caputo derivative; Asymptotic stability; Equilibrium point

Autoři

KISELA, T.; ČERMÁK, J.

Rok RIV

2016

Vydáno

09.05.2015

ISSN

0924-090X

Periodikum

NONLINEAR DYNAMICS

Svazek

80

Číslo

4

Stát

Spojené státy americké

Strany od

1673

Strany do

1684

Strany počet

12

BibTex

@article{BUT115853,
  author="Tomáš {Kisela} and Jan {Čermák}",
  title="Stability properties of two-term fractional differential equations",
  journal="NONLINEAR DYNAMICS",
  year="2015",
  volume="80",
  number="4",
  pages="1673--1684",
  doi="10.1007/s11071-014-1426-x",
  issn="0924-090X"
}