Approximate Controllability of Fractional Order Stochastic Variational Inequalities Driven by Poisson Jumps

This paper proposes the sufficient conditions of approximate controllability for a class of fractional order stochastic variational inequalities driven by Poisson jumps. The possibilities of finding the approximate controllability of a given problem of this type introduce the smoothing system corresponding to the fractional order stochastic variational inequalities driven by Poisson jumps. The results are achieved upon the Moreau-Yosida approximation of subdifferential operator. Sufficient conditions for the approximate controllability of smoothing system are discussed under the boundedness condition on control operator. The results are formulated and proved by using the fractional calculus, semigroup theory, stochastic analysis techniques. An example is provided to illustrate the obtained theory.