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Approximate controllability of fractional evolution inclusions with damping

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  • Li, Xuemei
  • Liu, Xinge
  • Tang, Meilan

Abstract

The approximate controllability of fractional evolution inclusions with damping is studied in this paper. Under a compactness assumption on the (α,μ)− regularized resolvent families of operators, some properties of operators associated with the regularized family are given. Next, the existence results of the system are obtained by nonlinear alternative of Leray-Schauder and Covitz and Nadler’s fixed point theorem. Furthermore, we obtain a new set of sufficient conditions for the approximate controllability of fractional evolution inclusions. Finally, examples are provided to illustrate the obtained results.

Suggested Citation

  • Li, Xuemei & Liu, Xinge & Tang, Meilan, 2021. "Approximate controllability of fractional evolution inclusions with damping," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921004276
    DOI: 10.1016/j.chaos.2021.111073
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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. Fan, Zhenbin, 2014. "Characterization of compactness for resolvents and its applications," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 60-67.
    3. Haq, Abdul & Sukavanam, N., 2020. "Existence and approximate controllability of Riemann-Liouville fractional integrodifferential systems with damping," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Mahmudov, N.I., 2020. "Finite-approximate controllability of semilinear fractional stochastic integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. 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.
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