Acta Mathematica Scientia

, Volume 39, Issue 1, pp 229–242 | Cite as

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

  • Xiuwen Li (李秀文)
  • Zhenhai Liu (刘振海)Email author
  • Jing Li (李景)
  • Chris Tisdell


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.

Key words

existence controllability fractional control systems damping regularized resolvent family 

2010 MR Subject Classification

34K05 34K30 35B35 93B05 47H10 


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Copyright information

© Wuhan Institutes of Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  • Xiuwen Li (李秀文)
    • 1
  • Zhenhai Liu (刘振海)
    • 1
    • 2
    Email author
  • Jing Li (李景)
    • 3
    • 4
  • Chris Tisdell
    • 5
  1. 1.School of ScienceNanjing University of Sciences and TechnologyNanjingChina
  2. 2.Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data ProcessingYulin Normal UniversityYulinChina
  3. 3.Hunan Province Key Laboratory of Mathematical Modelling and Analysis in EngineeringChangshaChina
  4. 4.Department of Mathematics and StatisticsChangsha University of Science and TechnologyChangshaChina
  5. 5.Faculty of ScienceThe University of New South Wales, UNSWSydneyAustralia

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