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Approximate controllability of fractional stochastic evolution equations. (English) Zbl 1238.93099
Summary: A class of dynamic control systems described by nonlinear fractional stochastic differential equations in Hilbert spaces is considered. Using fixed point technique, fractional calculations, stochastic analysis technique and methods adopted directly from deterministic control problems, a new set of sufficient conditions for approximate controllability of fractional stochastic differential equations is formulated and proved. In particular, we discuss the approximate controllability of nonlinear fractional stochastic control system under the assumptions that the corresponding linear system is approximately controllable. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result. Finally as a remark, the compactness of semigroup is not assumed and subsequently the conditions are obtained for exact controllability result.
MSC:
93E03General theory of stochastic systems
93B05Controllability
34A08Fractional differential equations
34G20Nonlinear ODE in abstract spaces
60H10Stochastic ordinary differential equations
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