The fractional PDE-ODE coupled system with Neumann boundary condition is considered in this paper. We design a boundary state feedback controller using the Backstepping method to stabilize the considered system. According to operator semigroup theory, we obtain a unique solution of the investigated system. Based on this, by using the fractional Lyapunov scheme, we prove that the system is Mittag-Leffler stable.
Fu et al. (Wed,) studied this question.