摘要
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.
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.
作者
Xiuwen LI
Zhenhai LIU
Jing LI
Chris TISDELL
李秀文;刘振海;李景;Chris TISDELL(School of Science, Nanjing University of Sciences and Technology;Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University;Hunan Province Key Laboratory of Mathematical Modelling and Analysis in Engineering;Department of Mathematics and Statistics, Changsha University of Science and Technology;Faculty of Science, The University of New South Wales, UNSW)
基金
NNSF of China(11671101,11661001)
NSF of Guangxi(2018GXNSFDA138002)
NSF of Hunan(2018JJ3519)
the funding from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie(823731CONMECH)
