Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$

In this study, the asymptotical stabilization problem of fuzzy fractional dynamic systems (FFDSs) with the semilinear form under the granular Caputo fractional derivative for the case \(q \in (1,2)\) is investigated. To tackle this, we propose a linear feedback controller aimed at stabilizing the unstable states of FFDSs. Taking advantage of the generalized fractional Laplace-like transform (GFLT) and the Gronwall-Bellman inequality, we provide a simple method to evaluate the stability of fractional dynamical systems. Finally, we validate the effectiveness of our approach through examples and corresponding simulations.