Successive approximation and optimal controls on fractional neutral stochastic differential equations with Poisson jumps

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