A General Maximum Principle for Discrete Fractional Stochastic Control System of Mean-Field Type

In this paper, we investigate a general maximum principle for discrete fractional stochastic difference system of mean-field type. The admissible control domain is nonconvex. We give Malliavin calculus for discrete-time case to deal with the fractional terms. The maximum principle of general type is derived by classical variation and linear operator methods. In addition, a linear-quadratic problem is solved to illustrate the main result and we also figure out a numerical result in this case.