A novel memristor-based chaotic system with fractional order

In 1971 L.O. Chua postulated the existence of a fourth circuit element, called memristor, but Williams´s group of HP Labs realized it only 37 years later. By looking at this promising research topic, in this paper a novel fractional-order system including a memristor is introduced. In particular, chaotic behaviors in the simplest fractional-order memristor-based system are shown. Numerical integrations and stability analysis of the system equilibria are carried out, with the aim to show that chaos can be found when the order of the derivative is 0.965. Finally, the presence of chaos is confirmed by the application of the recently introduced 0-1 test.