Optimal control of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps

In this work, the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hilfer fractional derivative. First, we study the existence and uniqueness of mild solution results are proved by the virtue of fractional calculus, successive approximation method and stochastic analysis techniques. Second, the optimal control of the proposed problem is presented by using Balder's theorem. Finally, an example is demonstrated to illustrate the obtained theoretical results.