The study investigates the Duffing oscillator with a fractional damping term, focusing on the interaction between the fractional order parameter and the damping parameter. The authors find that for specific values of these parameters and the forcing amplitude, high oscillation amplitudes can be induced, leading to resonance phenomena. This behavior is unique to systems with fractional damping and is not observed in traditional integer-order systems. The fractional damping term captures memory effects and non-local behavior, allowing for sub-diffusive or super-diffusive damping. The study uses numerical simulations to analyze the effects of the fractional order parameter on the oscillation amplitude, revealing resonance peaks that appear at certain values of the fractional order parameter and damping parameter. These peaks are confirmed by the $Q$-factor, which measures the amplification of the signal. The analysis also explores the impact of the forcing amplitude on the oscillation amplitude, showing that high forcing amplitudes can sustain high oscillation amplitudes over a larger parameter range. The study concludes that the fractional damping term introduces rich and complex dynamics, which can be crucial for understanding and predicting resonant behaviors in various physical systems, including viscoelastic and porous materials.The study investigates the Duffing oscillator with a fractional damping term, focusing on the interaction between the fractional order parameter and the damping parameter. The authors find that for specific values of these parameters and the forcing amplitude, high oscillation amplitudes can be induced, leading to resonance phenomena. This behavior is unique to systems with fractional damping and is not observed in traditional integer-order systems. The fractional damping term captures memory effects and non-local behavior, allowing for sub-diffusive or super-diffusive damping. The study uses numerical simulations to analyze the effects of the fractional order parameter on the oscillation amplitude, revealing resonance peaks that appear at certain values of the fractional order parameter and damping parameter. These peaks are confirmed by the $Q$-factor, which measures the amplification of the signal. The analysis also explores the impact of the forcing amplitude on the oscillation amplitude, showing that high forcing amplitudes can sustain high oscillation amplitudes over a larger parameter range. The study concludes that the fractional damping term introduces rich and complex dynamics, which can be crucial for understanding and predicting resonant behaviors in various physical systems, including viscoelastic and porous materials.