Fractional neutral stochastic integrodifferential equations with Caputo fractional derivative: Rosenblatt process, Poisson jumps and Optimal control

The objective of this paper is to investigate the existence mild solutions and optimal controls for a class fractional neutral stochastic integrodifferential equations driven by Rosenblatt process Poisson jumps in Hilbert spaces. First we establish new set sufficient conditions aforementioned systems using successive approximation approach. results are formulated proved calculus, solution operator analysis techniques. control pairs system governed differential poisson also been presented. An example provided illustrate theory.