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We consider the nonlinear Duffing oscillator in presence of fractionaldamping which is characteristic in different physical situations. The system isstudied with a smaller and larger damping parameter value, that we call theunderdamped and overdamped regimes. In both we have studied the relationbetween the fractional parameter, the amplitude of the oscillations and thetimes to reach the asymptotic behavior, called asymptotic times. In theoverdamped regime, the study shows that, also here, there are oscillations forfractional order derivatives and their amplitudes and asymptotic times cansuddenly change for small variations of the fractional parameter. In addition,in this latter regime, a resonant-like behavior can take place for suitablevalues of the parameters of the system. These results are corroborated bycalculating the corresponding Q-factor. We expect that these results can beuseful for a better understanding of fractional dynamics and its possibleapplications as in modeling different kind of materials that normally needcomplicated damping terms.

Fractional damping effects on the transient dynamics of the Duffing oscillator