Boundary stabilization of semi‐linear time fractional reaction–diffusion systems with delays

Abstract This paper examines the stabilization results for a class of semi‐linear time fractional reaction–diffusion partial differential equations (PDEs) with state delay using the backstepping method. The main goal is to design the boundary control for the system by proving the well‐posedness of the kernel function. The considered reaction–diffusion system is transformed into a stable target system using an invertible Volterra integral transformation. Also, the stability results in the sense of the Lyapunov–Krasovskii theory are proved and sufficient conditions are derived with the help of the linear matrix inequality (LMI) approach. Finally, the results are numerically validated with a fractional‐order Hutchinson's equation.