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Approximate controllability of semilinear evolution equations of fractional order with nonlocal and impulsive conditions via an approximating technique

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  • Ge, Fu-Dong
  • Zhou, Hua-Cheng
  • Kou, Chun-Hai

Abstract

This paper is concerned with the approximate controllability of the semilinear fractional evolution equations with nonlocal and impulsive conditions. Our main results are obtained by utilizing the technique of approximate solution and the theory of fixed point. In addition, the impulsive functions in this paper are supposed to be continuous and the nonlocal item is divided into two cases: Lipschitz continuous and only continuous, which generalizes the previous contributions. Finally two examples are worked out to illustrate our obtained results.

Suggested Citation

  • Ge, Fu-Dong & Zhou, Hua-Cheng & Kou, Chun-Hai, 2016. "Approximate controllability of semilinear evolution equations of fractional order with nonlocal and impulsive conditions via an approximating technique," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 107-120.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:107-120
    DOI: 10.1016/j.amc.2015.11.056
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    References listed on IDEAS

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    1. N. Sukavanam & Surendra Kumar, 2011. "Approximate Controllability of Fractional Order Semilinear Delay Systems," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 373-384, November.
    2. Balasubramaniam, P. & Tamilalagan, P., 2015. "Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 232-246.
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    Cited by:

    1. Cai, Ruiyang & Ge, Fudong & Chen, YangQuan & Kou, Chunhai, 2019. "Regional observability for Hadamard-Caputo time fractional distributed parameter systems," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 190-202.
    2. Mahmudov, N.I., 2020. "Finite-approximate controllability of semilinear fractional stochastic integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Mahmudov, N.I., 2018. "Partial-approximate controllability of nonlocal fractional evolution equations via approximating method," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 227-238.
    4. Arshi Meraj & Dwijendra N. Pandey, 2020. "Approximate controllability of non-autonomous Sobolev type integro-differential equations having nonlocal and non-instantaneous impulsive conditions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 501-518, June.

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