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International Journal of Differential Equations
Volume 2010 (2010), Article ID 197020, 12 pages
Linear Fractionally Damped Oscillator
Department of Mathematics, Monroe County Community College, Monroe, MI 48161-9746, USA
Received 8 July 2009; Accepted 11 August 2009
Academic Editor: Mark M. Meerschaert
Copyright © 2010 Mark Naber. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999.
- S. Burov and E. Barkai, “Fractional langevin equation: over-damped, under-damped, and critical behaviors,” http://arxiv.org/abs/0802.3777.
- S. Burov and E. Barkai, “The critical exponent of the fractional langevin equation is ,” http://arxiv.org/abs/0712.3407.
- G. M. Zaslavsky, A. A. Stanislavsky, and M. Edelman, “Chaotic and pseudochaotic attractors of perturbed fractional oscillator,” Chaos, vol. 16, no. 1, Article ID 013102.
- A. C. Galucio, J. FranÇois, and F. Dubois, “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 scheme,” Derivation fractionaire en mecanique—etat-de-l'art et applications, CNAM Paris, France, November 2006, http://www.cnam.fr/lmssc/seminaires/derivfrac/galucio/.
- B. N. Narahari Achar, J. W. Hanneken, and T. Clarke, “Damping characteristics of a fractional oscillator,” Physica A, vol. 339, no. 3-4, pp. 311–319, 2004.
- R. L. Bagley and P. J. Torvik, “On the appearance of the fractional derivative in the behavior of real materials,” Journal of Applied Mechanics, vol. 51, pp. 294–298, 1984.
- S. Saha Ray and R. K. Bera, “Analytical solution of the Bagley Torvik equation by Adomian decomposition method,” Applied Mathematics and Computation, vol. 168, no. 1, pp. 398–410, 2005.