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Existence and approximate controllability of Sobolev type fractional stochastic evolution equations

Mahmudov N. I.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2014

Vol. 62, nr 2

205--215

We study the existence of mild solutions and the approximate controllability concept for Sobolev type fractional semilinear stochastic evolution equations in Hilbert spaces. We prove existence of a mild solution and give sufficient conditions for the approximate controllability. In particular, we prove that the fractional linear stochastic system is approximately controllable in [0, b] if and only if the corresponding deterministic fractional linear system is approximately controllable in every [s, b], 0 ≤ s < b. An example is provided to illustrate the application of the obtained results.