Synchronization of Caputo‐Hadamard Fractional‐Order Competitive Neural Networks With Discrete and Distributed Delays

ABSTRACT This paper investigates the synchronization problem for Caputo–Hadamard fractional‐order competitive neural networks (CHFCNNs) with both discrete and distributed delays. First, a new lemma is established by employing Caputo–Hadamard fractional calculus theory and analytical techniques. Second, an adaptive hybrid controller and a linear controller are designed. By employing inequality techniques, leveraging properties of the Mittag‐Leffler function, and utilizing our established lemma, the criteria for both Mittag‐Leffler synchronization and complete synchronization are derived. Finally, the validity of the theoretical results is verified through numerical examples.