Mittag-Leffler synchronization of Caputo-Hadamard fractional-order BAM neural networks with and without distributed delays

This paper investigates the Mittag-Leffler synchronization (M-LS) for Caputo-Hadamard fractional-order (CHF) BAM neural networks (BAMNNs) with and without distributed delays. First, by applying the zero-point existence theorem and comparison principle, a new Halanay inequality is constructed, which is conducive to analyzing M-LS of CHF dynamical networks. Second, a new weighted-norm-based inequality on CHF derivative is rigorously derived based on Hölder’s inequality. Subsequently, by using our proposed inequalities and some inequality techniques, we derive sufficient M-LS conditions for the considered CHF BAMNNs under linear and nonlinear feedback controllers. Especially, a range of existing integer-order and fractional-order findings are subsumed into our results as special cases. Finally, two numerical simulations are provided to validate the theoretical results.