Optimal control for fractional stochastic differential system driven by fractional Brownian motion with Poisson jumps

Abstract

The objective of this article is to investigate the optimal controls for a class of fractional stochastic dierential system driven by fractional Brownian motion with Poisson jumps in Hilbert space setting. The sucient conditions for the existence of mild solution results are formulated and proved by virtue of fractional calculus, solution operator and stochastic analysis techniques. Furthermore, the existence of optimal control of the proposed problem is presented by using Balder's theorem. Finally, stochastic integrodierential equations are provided to validate the applicability of the derived theoretical results.