Approximate Controllability of Sobolev Type Fractional Stochastic Nonlocal Nonlinear Differential Equations in Hilbert Spaces

Debbouche, AmarBaleanu, DumitruKerboua, Mourad2017-03-152025-09-182017-03-152025-09-182014Kerboua, M., Debbouche, A., Baleanu, D. (2014). Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces. Electronic Journal Of Qualitative Theory Of Differential Equations, (58), 1-16.1417-3875https://doi.org/10.14232/ejqtde.2014.1.58https://hdl.handle.net/20.500.12416/13515Kerboua, Mourad/0000-0001-8244-0269We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Holder's inequality, 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 is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.eninfo:eu-repo/semantics/closedAccessApproximate ControllabilityFractional Sobolev Type EquationStochastic SystemFixed Point TechniqueFractional Stochastic Nonlocal ConditionHolder'S InequalityApproximate Controllability of Sobolev Type Fractional Stochastic Nonlocal Nonlinear Differential Equations in Hilbert SpacesApproximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spacesArticle10.14232/ejqtde.2014.1.582-s2.0-84916618623