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In this paper, we establish the existence and uniqueness of fully coupledforward-backward stochastic differential equations (FBSDEs in short) driven byanomalous sub-diffusions $B_{L_t}$ under suitable monotonicity conditions onthe coefficients. Here $B$ is a Brownian motion on $\bf R$ and $L_t:=\inf\{r>0: S_r>t\}$, $t\geq 0,$ is the inverse of a subordinator $S$ with drift$\kappa >0$ that is independent of $B$. Various a priori estimates on thesolutions of the FBSDEs are also presented.

Fully coupled forward-backward stochastic differential equations driven by sub-diffusions