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Zbl 1238.93099
Sakthivel, R.; Suganya, S.; Anthoni, S.M.
Approximate controllability of fractional stochastic evolution equations. (English)
[J] Comput. Math. Appl. 63, No. 3, 660-668 (2012). ISSN 0898-1221

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 2000:: *93E03 General theory of stochastic systems
93B05 Controllability
34A08
34G20 Nonlinear ODE in abstract spaces
60H10 Stochastic ordinary differential equations

Keywords: approximate controllability; stochastic systems; fractional differential equation; fixed point principle

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