Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in

Abstract. We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlin-ear differential equations of Sobolev type in Hilbert spaces. We use Hölder’s inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted di-rectly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results