Publication result detail

Stability properties of two-term fractional differential equations

KISELA, T.; ČERMÁK, J.

Original Title

Stability properties of two-term fractional differential equations

English Title

Stability properties of two-term fractional differential equations

Type

WoS Article

Original Abstract

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.

English abstract

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.

Keywords

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

Key words in English

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

Authors

KISELA, T.; ČERMÁK, J.

RIV year

2016

Released

09.05.2015

ISBN

0924-090X

Periodical

NONLINEAR DYNAMICS

Volume

80

Number

4

State

United States of America

Pages from

1673

Pages to

1684

Pages count

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"
}