Optimal feedback stabilization of fractional output in semilinear distributed systems

This study explores the stabilization of state–space fractional derivatives in semilinear distributed systems, using the Riemann–Liouville derivative of order $\alpha$, where $\alpha$ lies within the interval $\left(0,1\right)$. The main objective is to develop effective feedback control strategies that ensure both strong and weak stabilization of fractional outputs. Additionally, we tackle a fractional minimization problem to enhance the system’s performance. A numerical simulation example is provided to demonstrate the practical significance of the proposed stabilization theorems.