Exact Null Controllability of Sobolev-Type Hilfer Fractional Stochastic Differential Equations with Fractional Brownian Motion and Poisson Jumps

Abstract

In this paper, we establish sufficient conditions for exact null controllability of Sobolev type stochastic differential equations with fractional Brownian motion and Poisson jumps in Hilbert spaces, where the time fractional derivative is the Hilfer derivative. The exact null controllability result is derived by using fractional calculus, compact semigroup, fixed point theorem and stochastic analysis. Finally, an example is given to show the application of our results.