This study investigates the Duffing oscillator with a fractional damping term, focusing on how the fractional order parameter, damping parameter, and forcing amplitude influence its oscillations. The research reveals that the fractional damping term can induce resonance phenomena, leading to high oscillation amplitudes when specific combinations of these parameters are used. Unlike traditional damping, fractional damping accounts for memory effects and non-local behavior, allowing for sub-diffusive or super-diffusive damping. The study shows that the fractional order parameter can trigger complex dynamics, including resonance-like behavior, which is not observed in systems with integer-order damping. The Duffing oscillator with fractional damping is modeled using a fractional derivative in the damping term, leading to a system of three fractional differential equations. Numerical simulations demonstrate that the oscillation amplitude is significantly affected by the fractional order parameter, with resonance peaks appearing for certain values of the damping parameter and forcing amplitude. These peaks are associated with aperiodic orbits and complex dynamics in phase space. The study also shows that the oscillation amplitude can be enhanced by specific combinations of high forcing amplitude, high damping parameter, and specific fractional order parameter values. The results indicate that the fractional order parameter plays a crucial role in inducing resonance phenomena, which are not present in systems with integer-order damping. The study highlights the importance of fractional derivatives in modeling systems with memory and non-local behavior, such as viscoelastic materials and diffusion processes. The findings suggest that fractional damping can lead to rich and complex dynamics, including resonance and chaotic behavior, which can be useful in predicting and controlling complex behaviors in various physical systems. The research also emphasizes the need for further investigation into the conditions under which these resonance phenomena occur and the parameters that influence their amplitude and frequency.This study investigates the Duffing oscillator with a fractional damping term, focusing on how the fractional order parameter, damping parameter, and forcing amplitude influence its oscillations. The research reveals that the fractional damping term can induce resonance phenomena, leading to high oscillation amplitudes when specific combinations of these parameters are used. Unlike traditional damping, fractional damping accounts for memory effects and non-local behavior, allowing for sub-diffusive or super-diffusive damping. The study shows that the fractional order parameter can trigger complex dynamics, including resonance-like behavior, which is not observed in systems with integer-order damping. The Duffing oscillator with fractional damping is modeled using a fractional derivative in the damping term, leading to a system of three fractional differential equations. Numerical simulations demonstrate that the oscillation amplitude is significantly affected by the fractional order parameter, with resonance peaks appearing for certain values of the damping parameter and forcing amplitude. These peaks are associated with aperiodic orbits and complex dynamics in phase space. The study also shows that the oscillation amplitude can be enhanced by specific combinations of high forcing amplitude, high damping parameter, and specific fractional order parameter values. The results indicate that the fractional order parameter plays a crucial role in inducing resonance phenomena, which are not present in systems with integer-order damping. The study highlights the importance of fractional derivatives in modeling systems with memory and non-local behavior, such as viscoelastic materials and diffusion processes. The findings suggest that fractional damping can lead to rich and complex dynamics, including resonance and chaotic behavior, which can be useful in predicting and controlling complex behaviors in various physical systems. The research also emphasizes the need for further investigation into the conditions under which these resonance phenomena occur and the parameters that influence their amplitude and frequency.