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International Journal of Differential Equations
Volume 2011 (2011), Article ID 635165, 12 pages
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
1Department of Mathematics, Shanghai University, Shanghai 200444, China
2School of Mathematics and Computational Science, China University of Petroleum (East China), Qingdao 266555, China
3Electrical and Computer Engineering Department, Utah State University, Logan, UT 84322-4160, USA
Received 18 April 2011; Accepted 14 June 2011
Academic Editor: Fawang Liu
Copyright © 2011 Fengrong Zhang et al. 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.
Citations to this Article [18 citations]
The following is the list of published articles that have cited the current article.
- Chunhai Kou, Huacheng Zhou, and Changpin Li, “Existence And Continuation Theorems Of Riemann-Liouville Type Fractional Differential Equations,” International Journal Of Bifurcation And Chaos, vol. 22, no. 4, 2012.
- Hadi Delavari, Reza Ghaderi, and Shaher Momani, “Reply to "Comments on "Fuzzy fractional order sliding mode controller for n onlinear systems, Commun Nonlinear Sci Numer Simulat 15 (2010) 963-978"",” Communications In Nonlinear Science And Numerical Simulation, vol. 17, no. 10, pp. 4010–4014, 2012.
- Mohammad Reza Faieghi, Hadi Delavari, and Dumitru Baleanu, “A note on stability of sliding mode dynamics in suppression of fractional-order chaotic systems,” Computers and Mathematics with Applications, vol. 66, no. 5, pp. 832–837, 2013.
- A. G. Butkovskii, S. S. Postnov, and E. A. Postnova, “Fractional integro-differential calculus and its control-theoretical applications. II. Fractional dynamic systems: Modeling and hardware implementation,” Automation and Remote Control, vol. 74, no. 5, pp. 725–749, 2013.
- KeWei Liu, and Wei Jiang, “Uniform stability of fractional neutral systems: a Lyapunov-Krasovskii functional approach,” Advances in Difference Equations, 2013.
- Yanfen Lu, Ranchao Wu, and Zhiquan Qin, “Asymptotic stability of nonlinear fractional neutral singular systems,” Journal of Applied Mathematics and Computing, 2013.
- Margarita Rivero, Sergei V. Rogosin, José A. Tenreiro Machado, and Juan J. Trujillo, “Stability of Fractional Order Systems,” Mathematical Problems in Engineering, vol. 2013, pp. 1–14, 2013.
- Tore Bakka, and Hamid Reza Karimi, “H-infinity static output-feedback control design with constrained information for offshore wind turbine system,” Journal Of The Franklin Institute-Engineering And Applied Mathematics, vol. 350, no. 8, pp. 2244–2260, 2013.
- Guopei Chen, and Ying Yang, “Robust Finite-Time Stability of Fractional Order Linear Time-Varying Impulsive Systems,” Circuits, Systems, and Signal Processing, 2014.
- Hu Wang, Yongguang Yu, Guoguang Wen, and Shuo Zhang, “Stability Analysis of Fractional-Order Neural Networks with Time Delay,” Neural Processing Letters, vol. 42, no. 2, pp. 479–500, 2014.
- Sajjad Shoja Majidabad, Heydar Toosian Shandiz, and Amin Hajizadeh, “Nonlinear fractional-order power system stabilizer for multi-machine power systems based on sliding mode technique,” International Journal of Robust and Nonlinear Control, 2014.
- Sajjad Shoja Majidabad, Heydar Toosian Shandiz, and Amin Hajizadeh, “Decentralized sliding mode control of fractional-order large-scale nonlinear systems,” Nonlinear Dynamics, 2014.
- Giuseppe Papotto, Francesco Carrara, Alessandro Finocchiaro, and Giuseppe Palmisano, “A 90-nm CMOS 5-Mbps Crystal-Less RF-Powered Transceiver for Wireless Sensor Network Nodes,” Ieee Journal of Solid-State Circuits, vol. 49, no. 2, pp. 335–346, 2014.
- Manuel A. Duarte-Mermoud, Norelys Aguila-Camacho, Javier A. Gallegos, and Rafael Castro-Linares, “Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems,” Communications in Nonlinear Science and Numerical Simulation, 2014.
- Ranchao Wu, and Michal Fečkan, “Stability analysis of impulsive fractional-order systems by vector comparison principle,” Nonlinear Dynamics, 2015.
- Cruz Vargas-De-Leon, “Volterra-type Lyapunov functions for fractional-order epidemic systems,” Communications In Nonlinear Science And Numerical Simulation, vol. 24, no. 1-3, pp. 75–85, 2015.
- Tridip Sardar, Sourav Rana, and Joydev Chattopadhyay, “A mathematical model of dengue transmission with memory,” Communications In Nonlinear Science And Numerical Simulation, vol. 22, no. 1-3, pp. 511–525, 2015.
- Javier A. Gallegos, Manuel A. Duarte-Mermoud, Norelys Aguila-Camacho, and Rafael Castro-Linares, “On fractional extensions of Barbalat Lemma,” Systems & Control Letters, vol. 84, pp. 7–12, 2015.