Existence and controllability for stochastic evolution inclusions of Clarke's subdifferential type

In this paper, we investigate a class of stochastic evolution inclusions of Clarke's subdifferential type in Hilbert spaces. The existence of mild solutions and controllability results are given and proved by using stochastic analysis techniques, semigroup of operators theory, a fixed point theorem of multivalued maps and properties of generalized Clarke subdifferential. An example is included to illustrate the applicability of the main results

Solvability of control problem for fractional nonlinear differential inclusions with nonlocal conditions

In this paper, we study the approximate controllability of nonlocal fractional differential inclusions involving the Caputo fractional derivative of order q ∈ (1,2) in a Hilbert space. Utilizing measure of noncompactness and multivalued fixed point strategy, a new set of sufficient conditions is obtained to ensure the approximate controllability of nonlocal fractional differential inclusions when the multivalued maps are convex. Precisely, the results are developed under the assumption that the corresponding linear system is approximately controllable.   &nbsp

Global existence and controllability to a stochastic integro-differential equation

In this paper, we are focused upon the global uniqueness results for a stochastic integro-differential equation in Fréchet spaces. The main results are proved by using the resolvent operators combined with a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. As an application, a controllability result with one parameter is given to illustrate the theory