Existence And Controllability For Nonlinear Fractional Control Systems With Damping in Hilbert Spaces
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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 wordsexistence controllability fractional control systems damping regularized resolvent family
2010 MR Subject Classification34K05 34K30 35B35 93B05 47H10
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