Synchronization of fractional order memristor-based inertial neural networks with time delay

In this paper, the synchronization problem of fractional order memristor-based inertial neural networks are investigated. To facilitate the analysis, the set-valued mapping theory is applied to the discontinuity problem caused by memristor. Since fractional order memristive inertial neural networks have two fractional derivative terms, it is hard to analyze. To solve this problem, a special feedback controller is designed in this paper to offset the fractional derivative term between 0 and 1 and the stability theory of the fractional autonomous system is used to analyze the fractional derivative term between 1 and 2. Then some sufficient conditions for the synchronization of fractional order memristive inertial neural networks are established. Finally, the effectiveness of the conclusion is verified by an example.