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Existence And Controllability For Nonlinear Fractional Control Systems With Damping in Hilbert Spaces

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Abstract

In this paper, we are concerned with the existence of mild solution and controllability for a class of nonlinear fractional control systems with damping in Hilbert spaces. Our first step is to give the representation of mild solution for this control system by utilizing the general method of Laplace transform and the theory of (α, γ)-regularized families of operators. Next, we study the solvability and controllability of nonlinear fractional control systems with damping under some suitable sufficient conditions. Finally, two examples are given to illustrate the theory.

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Authors and Affiliations

  1. School of Science, Nanjing University of Sciences and Technology, Nanjing, 210094, China

    Xiuwen Li  (李秀文) & Zhenhai Liu  (刘振海)

  2. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, China

    Zhenhai Liu  (刘振海)

  3. Hunan Province Key Laboratory of Mathematical Modelling and Analysis in Engineering, Changsha, 410114, China

    Jing Li  (李景)

  4. Department of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410114, China

    Jing Li  (李景)

  5. Faculty of Science, The University of New South Wales, UNSW, Sydney, 2052, Australia

    Chris Tisdell

Authors
  1. Xiuwen Li  (李秀文)
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  2. Zhenhai Liu  (刘振海)
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  3. Jing Li  (李景)
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  4. Chris Tisdell
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Corresponding author

Correspondence to Zhenhai Liu  (刘振海).

Additional information

Project supported by NNSF of China (11671101, 11661001), NSF of Guangxi (2018GXNSFDA138002), NSF of Hunan (2018JJ3519) and the funding from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie (823731 CONMECH).

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Li, X., Liu, Z., Li, J. et al. Existence And Controllability For Nonlinear Fractional Control Systems With Damping in Hilbert Spaces. Acta Math Sci 39, 229–242 (2019). https://doi.org/10.1007/s10473-019-0118-5

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  • DOI: https://doi.org/10.1007/s10473-019-0118-5

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