Existence and uniqueness of solution for fully coupled fractional forward–backward stochastic differential equations with delay and anticipated term.

This paper deals with fully coupled fractional forward–backward stochastic differential equations (FBSDEs) with delay and anticipated term. In these equations the coefficients depend on not only the future state but also the past one. We investigate the existence and uniqueness result for such FBSDEs by using the method of continuation. We also obtain a comparison theorem. • An existence and uniqueness result for fractional FBSDEs is established. • The main result is proved by using the continuation method. • A comparison theorem for fractional AFBSDDEs is also presented. [ABSTRACT FROM AUTHOR]