Fateh, EllaggouneBaleanu, DumitruMourad, Kerboua2019-12-202025-09-182019-12-202025-09-182018Mourad, Kerboua; Fateh, Ellaggoune; Baleanu, Dumitru (2018). Stochastic fractional perturbed control systems with fractional Brownian motion and Sobolev stochastic non local conditions, Collectanea Mathematica, 69(2), 283-296.0010-07572038-4815https://doi.org/10.1007/s13348-017-0207-5https://hdl.handle.net/20.500.12416/14629Kerboua, Mourad/0000-0001-8244-0269This paper investigates the approximate controllability for Sobolev type stochastic perturbed control systems of fractional order with fractional Brownian motion and Sobolev fractional stochastic nonlocal conditions in a Hilbert space, A new set of sufficient conditions are established by using semigroup theory, fractional calculus, stochastic integrals for fractional Brownian motion, Banach's fixed point theorem. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is also given to illustrate the obtained theory.eninfo:eu-repo/semantics/openAccessApproximate ControllabilityPerturbed Control SystemsFractional Stochastic SystemFixed Point TechniqueStochastic Nonlocal ConditionFractional Brownian MotionArticle10.1007/s13348-017-0207-52-s2.0-85044969469