- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 610547, 4 pages
Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality
School of Mathematical Sciences, Anhui University, Hefei 230039, China
Received 22 October 2013; Accepted 2 January 2014; Published 23 February 2014
Academic Editor: Irena Rachůnková
Copyright © 2014 Pang Denghao and Jiang Wei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- K. Zhang and D. Q. Cao, “Further results on asymptotic stability of linear neutral systems with multiple delays,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 344, no. 6, pp. 858–866, 2007.
- D. Q. Cao and P. He, “Stability criteria of linear neutral systems with a single delay,” Applied Mathematics and Computation, vol. 148, no. 1, pp. 135–143, 2004.
- P. T. Nam and V. N. Phat, “An improved stability criterion for a class of neutral differential equations,” Applied Mathematics Letters, vol. 22, no. 1, pp. 31–35, 2009.
- P. Balasubramaniam, R. Krishnasamy, and R. Rakkiyappan, “Delay-dependent stability of neutral systems with time-varying delays using delay-decomposition approach,” Applied Mathematical Modelling, vol. 36, no. 5, pp. 2253–2261, 2012.
- F. Wang, “Exponential asymptotic stability for nonlinear neutral systems with multiple delays,” Nonlinear Analysis: Real World Applications, vol. 8, no. 1, pp. 312–322, 2007.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999.
- A. Anatoly Kilbas and H. M. Srivastava, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006.
- T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer, Berlin, Germany, 2011.
- Y. Zhou, F. Jiao, and J. Li, “Existence and uniqueness for fractional neutral differential equations with infinite delay,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 3249–3256, 2009.
- S. Liu, X. Li, W. Jiang, and X. Zhou, “Mittag-Leffler stability of nonlinear fractional neutral singular systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 10, pp. 3961–3966, 2012.
- X.-F. Zhou, J. Wei, and L.-G. Hu, “Controllability of a fractional linear time-invariant neutral dynamical system,” Applied Mathematics Letters, vol. 26, no. 4, pp. 418–424, 2013.
- S. Liu and W. Jiang, “Asymptotic stability of nonlinear descriptor systems with infinite delays,” Annals of Differential Equations, vol. 26, no. 2, pp. 174–180, 2010.
- Z. Zhang and J. Wei, “Some results of the degenerate fractional differential system with delay,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1284–1291, 2011.
- M. P. Lazarević, “Finite time stability analysis of fractional control of robotic time-delay systems,” Mechanics Research Communications, vol. 33, no. 2, pp. 269–279, 2006.
- C. Bonnet and J. R. Partington, “Analysis of fractional delay systems of retarded and neutral type,” Automatica, vol. 38, no. 8, pp. 1133–1138, 2002.
- X. Zhang, “Some results of linear fractional order time-delay system,” Applied Mathematics and Computation, vol. 197, no. 1, pp. 407–411, 2008.
- M. P. Lazarević and A. M. Spasić, “Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach,” Mathematical and Computer Modelling, vol. 49, no. 3-4, pp. 475–481, 2009.
- H. Ye, J. Gao, and Y. Ding, “A generalized Gronwall inequality and its application to a fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 328, no. 2, pp. 1075–1081, 2007.