Publication detail

Stability properties of two-term fractional differential equations

KISELA, T. ČERMÁK, J.

Original Title

Stability properties of two-term fractional differential equations

Type

journal article in Web of Science

Language

English

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.

Keywords

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

Authors

KISELA, T.; ČERMÁK, J.

RIV year

2015

Released

9. 5. 2015

ISBN

0924-090X

Periodical

NONLINEAR DYNAMICS

Year of study

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"
}