  We consider a mean-field optimal control problem for stochastic differential
equations with delay driven by fractional Brownian motion with Hurst parameter
greater than one half. Stochastic optimal control problems driven by fractional
Brownian motion can not be studied using classical methods, because the
fractional Brownian motion is neither a Markov process nor a semi-martingale.
However, using the fractional White noise calculus combined with some special
tools related to the differentiation for functions of measures, we establish
and prove necessary and sufficient stochastic maximum principles. To illustrate
our study, we consider two applications: we solve a problem of optimal
consumption from a cash flow with delay and a linear-quadratique (LQ) problem
with delay.
