EXISTENCE AND CONTROLLABILITY FOR NONLINEAR FRACTIONAL CONTROL SYSTEMS WITH DAMPING IN HILBERT SPACES

doi:10.1007/s10473-019-0118-5

Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (1): 229-242.doi: 10.1007/s10473-019-0118-5

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EXISTENCE AND CONTROLLABILITY FOR NONLINEAR FRACTIONAL CONTROL SYSTEMS WITH DAMPING IN HILBERT SPACES

Xiuwen LI¹, Zhenhai LIU^1,2, Jing LI³, Chris TISDELL⁴

1. School of Science, Nanjing University of Sciences and Technology, Nanjing 210094, China;
2. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China;
3. Hunan Province Key Laboratory of Mathematical Modelling and Analysis in Engineering;Department of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China;
4. Faculty of Science, The University of New South Wales, UNSW, Sydney 2052, Australia

Received:2017-04-10 Revised:2017-09-16 Online:2019-02-25 Published:2019-03-13
Contact: Zhenhai LIU E-mail:zhhliu@hotmail.com
Supported by:
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).

Abstract

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.

Key words: existence, controllability, fractional control systems, damping, regularized resolvent family

Xiuwen LI, Zhenhai LIU, Jing LI, Chris TISDELL. EXISTENCE AND CONTROLLABILITY FOR NONLINEAR FRACTIONAL CONTROL SYSTEMS WITH DAMPING IN HILBERT SPACES[J].Acta mathematica scientia,Series B, 2019, 39(1): 229-242.

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References

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EXISTENCE AND CONTROLLABILITY FOR NONLINEAR FRACTIONAL CONTROL SYSTEMS WITH DAMPING IN HILBERT SPACES

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