This paper included a detailed discussion of the delayed fractional-order neural networks (FONNs) subject to impulse effects as well as their fixed-time synchronization (FXTS) problem. To explore this issue, an advanced fixed-time stability (FTS) is introduced, which considers the impact of order \(\alpha \) on settling-time (ST), allows time-varying functions for the coefficients and indefinite derivatives of the Lyapunov function (LF). Next, several measures are adopted to handle issues in control systems. Firstly, a piecewise function is utilized within the integral function to avoid integral windup. Secondly, a class of fractional-order integral sliding mode control (FOSMC) and a class of fractional-order integral sliding mode surface (FOSMS) with odd power characteristics are designed. This design addresses the chattering problem resulting from the sign function and enables the fixed-time reachability and stability of the sliding mode dynamics. Subsequently, several relevant conditions were obtained to solve the FXTS problem of FONNs with impulse effects. At last, to verify the effectiveness of the theoretical results, a numerical simulation is provided.
