New Fixed-Time Stability Theorems for Delayed Fractional-Order Systems and Applications

This paper examines the problem of improved fixed-time stability for generalized delayed fractional-order systems (FOSs). As a first step, some conditions are presented in two theorems to verify (F-TS) FOSs by using Lyapunov theory and indefinite functionals, where derivative functions may not exist. Furthermore, corresponding estimated settling time is also provided. Second, results extended study neural networks (FONNs) with time-delays synchronization. Using Dirac delta functions, we propose an explicit saturated impulsive controller synchronize master slave systems. Moreover, constructing suitable Lyapunov-Krasovskii (LKF), derive algebraic guarantee synchronization addressed FONNs. The simulation demonstrate feasibility efficacy proposed method.