Stabilization of impulsive fuzzy dynamic systems involving Caputo short-memory fractional derivative

The main focus of this paper is to investigate the asymptotic stability of impulsive fuzzy fractional dynamic systems (IFFDSs) under the Caputo fractional derivative concept in the short-memory sense. To address the issue of asymptotic instability in IFFDSs, a linear feedback controller is introduced. The paper proposes two methods for achieving this, namely Lyapunov’s direct method (LDM) which is known for its high efficiency in surveying the stability theory of dynamic systems, and the direct evaluation method (DEM), which utilizes the properties of the Laplace transform, the Mittag–Leffler function, and Gronwall–Bellman inequality. The effectiveness of the proposed methods is demonstrated through numerical examples.