Fractional dynamics and synchronization of Kuramoto oscillators with nonlocal, nonsingular and strong memory

Abstract

This work deals with the synchronization of fractional order Kuramoto oscillator. The main idea is to prove that, using fractional derivatives we can get synchronization in a Kuramoto system when the critical gain value is under the computed value. The Atangana-Baleanu-Caputo derivative is used to prove the synchronization in a system with 5, 10 and 45 coupled oscillators. The analysis developed in the present work proves that even when we use a lower value of the critical gain, we can get synchronization in some oscillator. We present the numerical solution using the Adams method.

Keywords

• Fractional derivative
• Fractional Kuramoto oscillators
• Synchronization
• Atangana-Baleanu derivative
• Adams method