Stability properties of two-term fractional differential equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F15%3APU115159" target="_blank" >RIV/00216305:26210/15:PU115159 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11071-014-1426-x" target="_blank" >http://dx.doi.org/10.1007/s11071-014-1426-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11071-014-1426-x" target="_blank" >10.1007/s11071-014-1426-x</a>

Result language
angličtina
Original language name
Stability properties of two-term fractional differential equations
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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