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Journal of Applied Mathematics
Volume 2012, Article ID 879657, 14 pages
http://dx.doi.org/10.1155/2012/879657
Research Article

Asymptotic Stability Results for Nonlinear Fractional Difference Equations

Department of Mathematics, Xiangnan University, Chenzhou 423000, China

Received 1 August 2011; Revised 27 December 2011; Accepted 2 January 2012

Academic Editor: Michela Redivo-Zaglia

Copyright © 2012 Fulai Chen and Zhigang Liu. 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.

  • Dorota Mozyrska, Malgorzata Wyrwas, and Ewa Pawluszewicz, “Stabilization of linear multi-parameter fractional difference control systems,” 2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 315–319, . View at Publisher · View at Google Scholar
  • Lourdu Marian, Reni Sagayaraj, George Maria Selvam, and Paul Loganathan, “Oscillation of Caputo like discrete fractional equations,” International Journal of Pure and Applied Mathematics, vol. 89, no. 5, pp. 667–677, 2013. View at Publisher · View at Google Scholar
  • 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. View at Publisher · View at Google Scholar
  • Yong Zhou, and Fulai Chen, “Existence and Ulam Stability of Solutions for Discrete Fractional Boundary Value Problem,” Discrete Dynamics In Nature And Society, 2013. View at Publisher · View at Google Scholar
  • Ewa Pawłuszewicz, and Dorota Mozyrska, “Local controllability of multi-term semi-linear control systems with the Caputo-type fractional difference operator,” 2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014, pp. 146–151, 2014. View at Publisher · View at Google Scholar
  • Małgorzata Wyrwas, Dorota Mozyrska, Malgorzata Wyrwas, and Dorota Mozyrska, “On mittag–leffler stability of fractional order difference systems,” Lecture Notes in Electrical Engineering, vol. 320, pp. 209–220, 2015. View at Publisher · View at Google Scholar
  • Małgorzata Wyrwas, Ewa Pawluszewicz, and Ewa Girejko, “Stability of nonlinear h-difference systems with n fractional orders,” Kybernetika, vol. 54, no. 1, pp. 112–136, 2015. View at Publisher · View at Google Scholar
  • Jaganmohan Jonnalagadda, “Analysis of a system of nonlinear fractional nabla difference equations,” International Journal of Dynamical Systems and Differential Equations, vol. 5, no. 2, pp. 149–174, 2015. View at Publisher · View at Google Scholar
  • Pitcha Khamsuwan, and Suwat Kuntanapreeda, “A Linear Matrix Inequality Approach to Output Feedback Control of Fractional-Order Unified Chaotic Systems with One Control Input,” Journal of Computational and Nonlinear Dynamics, vol. 11, no. 5, 2016. View at Publisher · View at Google Scholar
  • Viorica Mariela Ungureanu, and Mădălina Roxana Buneci, “Mean Square Stability of Discrete-Time Fractional Order Systems With Multiplicative Noise,” Theory and Applications of Non-integer Order Systems, vol. 407, pp. 123–133, 2016. View at Publisher · View at Google Scholar
  • Dorota Mozyrska, and Małgorzata Wyrwas, “Explicit criteria for stability of fractional h-difference two-dimensional systems,” International Journal of Dynamics and Control, 2016. View at Publisher · View at Google Scholar
  • Dorota Mozyrska, and Małgorzata Wyrwas, “Stability by linear approximation and the relation between the stability of difference and differential fractional systems,” Mathematical Methods in the Applied Sciences, 2016. View at Publisher · View at Google Scholar
  • Wei Nian Li, “Oscillation results for certain forced fractional difference equations with damping term,” Advances in Difference Equations, vol. 2016, no. 1, 2016. View at Publisher · View at Google Scholar
  • Weihong Sheng, and Wei Nian Li, “Forced oscillation for solutions of boundary value problems of fractional partial difference equations,” Advances in Difference Equations, vol. 2016, no. 1, 2016. View at Publisher · View at Google Scholar
  • He-Ping Xie, Guo-Cheng Wu, Dumitru Baleanu, and Fu-Lai Chen, “Chaos synchronization of fractional chaotic maps based on the stability condition,” Physica A: Statistical Mechanics and its Applications, vol. 460, pp. 374–383, 2016. View at Publisher · View at Google Scholar
  • Dumitru Baleanu, Guo–Cheng Wu, Yun–Ru Bai, and Fu–Lai Chen, “Stability analysis of Caputo–like discrete fractional systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 48, pp. 520–530, 2017. View at Publisher · View at Google Scholar
  • Piotr Ostalczyk, Marcin Bąkała, and Jacek Nowakowski, “State Delays Extraction in the Fractional-Order State-Space Model,” Non-Integer Order Calculus and its Applications, vol. 496, pp. 204–216, 2018. View at Publisher · View at Google Scholar
  • Mark Edelman, “On stability of fixed points and chaos in fractional systems,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 28, no. 2, pp. 023112, 2018. View at Publisher · View at Google Scholar