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Approximate controllability of Sobolev type nonlocal fractional stochastic dynamic systems in Hilbert spaces. (English) Zbl 1291.93039

Summary: We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.

MSC:

93B05 Controllability
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
34A08 Fractional ordinary differential equations
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