Global Mittag-Leffler synchronization of fractional-order neural networks with discontinuous activations

• Discontinuous activations are taken into account in fractional-order neural networks.
• Filippov solution is introduced to study the dynamics behavior of fractional-order neural networks with discontinuous activations (FNNDAs).
• Prove the existence of global solution in the sense of Filippov for FNNDAs based on a singular Gronwall inequality.
• Some sufficient conditions on global Mittag-Leffler synchronization of FNNDAs are obtained.

This paper is concerned with the global Mittag-Leffler synchronization for a class of fractional-order neural networks with discontinuous activations (FNNDAs). We give the concept of Filippov solution for FNNDAs in the sense of Caputo’s fractional derivation. By using a singular Gronwall inequality and the properties of fractional calculus, the existence of global solution under the framework of Filippov for FNNDAs is proved. Based on the nonsmooth analysis and control theory, some sufficient criteria for the global Mittag-Leffler synchronization of FNNDAs are derived by designing a suitable controller. The proposed results enrich and enhance the previous reports. Finally, one numerical example is given to demonstrate the effectiveness of the theoretical results.