References

Achar, B.N.N., J.W. Hanneken and T. Clarke, 2004. Damping characteristics of a fractional oscillator. Phys. A Stat. Mech. Appl., 339: 311-319.
CrossRef  |  

Andrianov, I.V. and W.T. van Horssen, 2006. Analytical approximations of the period of a generalizednonlinear van der Pol oscillator. J. Sound Vib., 295: 1099-1104.
CrossRef  |  

Andronov, A., A.A. Vitt and S.E. Hajkin, 1981. Teorija Kolebanij. Nauka publishers, Moskva, Russia.

Burov, S. and E. Barkai, 2007. The critical exponent of the fractional langevin equation is αc-0.402. http://arxiv.org/abs/0712.3407.

Burov, S. and E. Barkai, 2008. Fractional langevin equation: Over-damped, under-damped and critical behaviors. http://arxiv.org/abs/0802.3777

Cveticanin, L., 2004. Vibrations of the nonlinear oscillator with quadratic nonlinearity. Physica A Stat. Mech. Appl., 341: 123-135.
CrossRef  |  

Cveticanin, L., 2009. Oscillator with strong quadratic damping force. Publ. Del'Institut Math., 85: 119-130.
CrossRef  |  

Galucio, A.C., J.F. Deu and F. Dubois, 2006. On the use of fractional derivative operators to describe viscoelastic damping in structural dynamics-FE formulation of sandwich beams and approximation of fractional derivatives by using the G^α scheme. Derivation Fractionnaire en Mecanique-Etat-de-L'art et Applications, CNAM, Paris, 17th November, 2006.

Mickens, R.E., 2002. Analysis of non-linear oscillators having non-polynomial elastic terms. J. Sound Vib., 255: 789-792.
Direct Link  |  

Naber, M., 2009. Linear fractionally damped oscillator. Int. J. Differ. Equations, 2010: 12-12.
CrossRef  |  

Nayfeh, A.H. and D.T. Mook, 1979. Nonlinear Oscillations. Wiley, New York, ISBN: 9780471035558, Pages: 720.

Pilipchuk, V.N., 2007. Strongly nonlinear vibrations of damped oscillators with two nonsmoothlimits. J. Sound Vib., 302: 398-402.
CrossRef  |  

Podlubny, I., 1999. Fractional Differential Equations. Vol. 198, Academic Press, San Diego, Calif, USA., ISBN: 9780125588409, Pages: 340.

Timoshenko, S., D.H. Young and W. Weaver, 1974. Vibration Problems in Engineering. 4th Edn., John Wiley and Sons, New York, ISBN: 0471873152.

Waluya, S.B. and W.T. van Horssen, 2003. On the periodic solutions of a generalized non-linear vander pol oscillator. J. Sound Vib., 268: 209-215.
Direct Link  |  

Zaslavsky, G.M., A.A. Stanislavsky and M. Edelman, 2006. Chaotic and pseudochaotic attractors of perturbed fractional oscillator. Chaos, 16: 20-20.
CrossRef  |  PubMed  |