Spatial $$\beta $$ -fractional output stabilization of bilinear systems with a time $$\alpha $$ -fractional-order

This research aims to investigate the stabilization problem of the Riemann-Liouville spatial \(\beta \)-fractional output with order \(\beta \in (0,\ 1)\) for a class of bilinear dynamical systems with a time Caputo \(\alpha \)-fractional derivative. Initially, we provide definitions and establish the well-posedness of the problem addressed. Furthermore, we introduce a feedback control strategy that ensures both weak and strong stabilization of the \(\beta \)-fractional output, under a broad set of sufficient conditions. Additionally, we present numerical computations to elucidate the effectiveness of the obtained results.