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

We 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 Hölder'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

Enlarged Controllability of Riemann-Liouville Fractional Differential Equations

We investigate exact enlarged controllability for time fractional diffusion systems of Riemann-Liouville type. The Hilbert uniqueness method is used to prove exact enlarged controllability for both cases of zone and pointwise actuators. A penalization method is given and the minimum energy control is characterized.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Nonlinear Dynamics', ISSN 1555-1415, eISSN 1555-1423, CODEN JCNDDM, available at [http://computationalnonlinear.asmedigitalcollection.asme.org]. Submitted 10-Aug-2017; Revised 28-Sept-2017 and 24-Oct-2017; Accepted 05-Nov-201