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Center stable manifold for planar fractional damped equations

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  • Wang, JinRong
  • Fĕckan, Michal
  • Zhou, Yong

Abstract

In this paper, we discuss the existence of a center stable manifold for planar fractional damped equations. By constructing a suitable Lyapunov–Perron operator via giving asymptotic behavior of Mittag–Leffler function, we obtain an interesting center stable manifold theorem. Finally, an example is provided to illustrate the result.

Suggested Citation

  • Wang, JinRong & Fĕckan, Michal & Zhou, Yong, 2017. "Center stable manifold for planar fractional damped equations," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 257-269.
    • Handle: RePEc:eee:apmaco:v:296:y:2017:i:c:p:257-269
    DOI: 10.1016/j.amc.2016.10.014
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    References listed on IDEAS

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    1. Balachandran, K. & Govindaraj, V. & Rivero, M. & Trujillo, J.J., 2015. "Controllability of fractional damped dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 66-73.
    2. Wang, JinRong & Ibrahim, Ahmed Gamal & Fečkan, Michal, 2015. "Nonlocal impulsive fractional differential inclusions with fractional sectorial operators on Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 103-118.
    3. JinRong Wang & Zhenbin Fan & Yong Zhou, 2012. "Nonlocal Controllability of Semilinear Dynamic Systems with Fractional Derivative in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 292-302, July.
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    Cited by:

    1. Yong Zhou & Jia Wei He & Bashir Ahmad & Ahmed Alsaedi, 2018. "Existence and Attractivity for Fractional Evolution Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-9, January.
    2. Haq, Abdul & Sukavanam, N., 2020. "Existence and approximate controllability of Riemann-Liouville fractional integrodifferential systems with damping," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Li, Xuemei & Liu, Xinge & Tang, Meilan, 2021. "Approximate controllability of fractional evolution inclusions with damping," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

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