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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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