Designing boundary feedback control improves stability in fractional PDE-ODE systems under Neumann conditions, highlighting new stabilization strategies.
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.
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Fu et al. (2025) studied this question.
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