Finite time stability of fractional delay differential equations

被引：186

作者：

Li, Mengmeng ^{[1
]}

Wang, JinRong ^{[1
]}

机构：

[1] Guizhou Univ, Dept Math, Guiyang 550025, Guizhou, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2017年 / 64卷

基金：

中国国家自然科学基金;

关键词：

Delayed Mittag-Leffler type matrix; Fractional delay differential; equations; Finite time stability; NEURAL-NETWORKS; SYSTEMS; EXISTENCE; MATRICES;

D O I：

10.1016/j.aml.2016.09.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we firstly introduce a concept of delayed Mittag-Leffler type matrix function, an extension of Mittag-Leffler matrix function for linear fractional ODEs, which help us to seek explicit formula of solutions to fractional delay differential equations by using the variation of constants method. Secondly, we present the finite time stability results by virtue of delayed Mittag-Leffler type matrix. Finally, an example is given to illustrate our theoretical results. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：170 / 176

页数：7

共 18 条

[1] Existence and stability results for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes quadratic integral equations
Abbas, S.
Benchohra, M.
Rivero, M.
Trujillo, J. J.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 247 : 319 - 328
[2] [Anonymous], 2006, THEORY APPL FRACTION
[3] Fredholm's boundary-value problems for differential systems with a single delay
Boichuk, A.
Diblik, J.
Khusainov, D.
Ruzickova, M.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (05) : 2251 - 2258
[4] .Representation of solutions of linear discrete systems with constant coefficients and pure delay
Diblik, J.
Khusainov, D. Ya.
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2006, 2006 (1)
[5] Representation of solutions of discrete delayed system x(k+1)=Ax(k)+Bx(k-m)+f(k) with commutative matrices
Diblík, J
Khusainov, DY
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 318 (01) : 63 - 76
[6] Exponential stability of linear discrete systems with constant coefficients and single delay
Diblik, J.
Khusainov, D. Ya.
Bastinec, J.
Sirenko, A. S.
[J]. APPLIED MATHEMATICS LETTERS, 2016, 51 : 68 - 73
[7] Finite-time stability of impulsive fractional-order systems with time-delay
Hei, Xindong
Wu, Ranchao
[J]. APPLIED MATHEMATICAL MODELLING, 2016, 40 (7-8) : 4285 - 4290
[8] Khusainov DY., 2003, Stud Univ ilina, V17.1, P101
[9] Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach
Lazarevic, Mihailo P.
Spasic, Aleksandar M.
[J]. MATHEMATICAL AND COMPUTER MODELLING, 2009, 49 (3-4) : 475 - 481
[10] Lyapunov stability analysis of fractional nonlinear systems
Liu, Song
Jiang, Wei
Li, Xiaoyan
Zhou, Xian-Feng
[J]. APPLIED MATHEMATICS LETTERS, 2016, 51 : 13 - 19

← 1 2 →