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Exponential stability and stabilization of fractional stochastic degenerate evolution equations in a Hilbert space.

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FD2W01 - Deterministic and stochastic fractional diļ¬€erential equations and jump processes

Authors: Arzu Ahmadova, Nazim Mahmudov, Juan J. Nieto Abstract: In this paper, we obtain a closed-form representation of a mild solution to the fractional stochastic degenerate evolution equation in a Hilbert space using the subordination principle and semigroup theory.  We study aforesaid abstract frational stochastic Cauchy problem with nonlinear state-dependent terms and show that if the Sobolev type resolvent families describing the linear part of the model are exponentially stable, then the whole system retains this property under some Lipschitz continuity assumptions for nonlinearity. We also establish conditions for stabilizability and prove that the fractional stochastic nonlinear Cauchy problem is exponentially stabilizable when the stabilizer acts linearly on the control systems. Finally, we provide applications to show the validity of our theory.

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