2015
DOI: 10.1016/j.amc.2014.12.010
|View full text |Cite
|
Sign up to set email alerts
|

Razumikhin-type stability theorems for functional fractional-order differential systems and applications

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
2

Citation Types

0
50
0

Year Published

2015
2015
2022
2022

Publication Types

Select...
6

Relationship

0
6

Authors

Journals

citations
Cited by 83 publications
(50 citation statements)
references
References 21 publications
0
50
0
Order By: Relevance
“…Moreover, many systems modelled with the help of fractional calculus display rich fractional dynamical behavior, such as viscoelastic systems [10], boundary layer effects in ducts [11], electromagnetic waves [12], fractional kinetics [13,14], and electrode-electrolyte polarization [15,16]. Many stability conditions have been proposed for linear fractional-order systems [17][18][19][20][21][22][23], fractional-order nonlinear systems [24][25][26][27][28][29][30], fractional-order neural networks [31,32], fractional-order switched linear systems [33,34], fractional-order singular systems [35,36], positive fractional-order systems [37,38] and fractional chaotic complex networks systems [39]. Many stability conditions have been proposed for linear fractional-order systems [17][18][19][20][21][22][23], fractional-order nonlinear systems [24][25][26][27][28][29][30], fractional-order neural ne...…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Moreover, many systems modelled with the help of fractional calculus display rich fractional dynamical behavior, such as viscoelastic systems [10], boundary layer effects in ducts [11], electromagnetic waves [12], fractional kinetics [13,14], and electrode-electrolyte polarization [15,16]. Many stability conditions have been proposed for linear fractional-order systems [17][18][19][20][21][22][23], fractional-order nonlinear systems [24][25][26][27][28][29][30], fractional-order neural networks [31,32], fractional-order switched linear systems [33,34], fractional-order singular systems [35,36], positive fractional-order systems [37,38] and fractional chaotic complex networks systems [39]. Many stability conditions have been proposed for linear fractional-order systems [17][18][19][20][21][22][23], fractional-order nonlinear systems [24][25][26][27][28][29][30], fractional-order neural ne...…”
Section: Introductionmentioning
confidence: 99%
“…As a result, the problem of stability analysis and control of fractional-order systems is an important problem in the theory and applications of fractional calculus. Many stability conditions have been proposed for linear fractional-order systems [17][18][19][20][21][22][23], fractional-order nonlinear systems [24][25][26][27][28][29][30], fractional-order neural networks [31,32], fractional-order switched linear systems [33,34], fractional-order singular systems [35,36], positive fractional-order systems [37,38] and fractional chaotic complex networks systems [39]. Among the reported methods, the Lyapunov direct method provides an effective approach to analyze the stability of fractional nonlinear systems.…”
Section: Introductionmentioning
confidence: 99%
“…The most frequently used definitions for noninteger derivatives are Riemann-Liouville, Grünwald-Letnikov, and Caputo definitions [6,9,[23][24][25][26][27][28][29][30][31][33][34][35][36][37][38]. As the Caputo fractional operator is more consistent than another ones, then this operator will be employed in the rest of this paper.…”
Section: Remarkmentioning
confidence: 99%
“…In [27], sufficient stability conditions for fractional-order epidemic systems have been obtained by Volterra-type Lyapunov functions. In [28,39], stability analysis problem of fractional-order systems with delays have been solved by Lyapunov approaches, Razumikhin-type stability theorems, and Lyapunov-Krasovskii approaches. In [64], simple criteria of Mittag-Leffler stability have been proposed for fractional nonlinear systems.…”
Section: Remark 13mentioning
confidence: 99%
See 1 more Smart Citation