Time delay effects on collective resonant behaviors in two coupled fractional oscillators with mass fluctuations.

In this study, we introduce a coupled fractional system consisting of two fluctuating-mass oscillators with time delay and investigate their collective resonant behaviors. First, we achieve complete synchronization between the average behaviors of these oscillators. We then derive the exact analytical expression for the output amplitude gain, and based on this, we observe generalized stochastic resonance (GSR) in the system. We further examine how GSR behavior depends on system parameters, demonstrating that coupling strength, fractional order, and time delay are crucial in facilitating and optimizing its intensity. Finally, numerical simulations are conducted to validate the analytical results.