Motivated by applications in population models, we consider S-asymptotically periodic solution of fractional differential equations with periodic environment forces or asymptotically periodic ones. The system is quasi-monotone, and the existence of positive S-asymptotically periodic solution is established by using upper and lower solutions. The sufficient conditions that ensure the uniqueness of positive S-asymptotically periodic solution are also established on the basis of theory of sublinear operator. The applications of the general conclusions to classical population models yield the global convergence of positive S-asymptotically periodic solution in logistic equation with or without weak Allee effect, and the model of two cooperative populations.