In this paper, we establish the existence and uniqueness of fully coupled
forward-backward stochastic differential equations (FBSDEs in short) driven by
anomalous sub-diffusions BLt under suitable monotonicity conditions on
the coefficients. Here B is a Brownian motion on R and Lt:=inf{r>0:Sr>t}, t≥0, is the inverse of a subordinator S with drift
κ>0 that is independent of B. Various a priori estimates on the
solutions of the FBSDEs are also presented