# On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator

@article{Camargo2009OnAD, title={On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator}, author={R. F. Camargo and E. C. Oliveira and J. Vaz}, journal={Journal of Mathematical Physics}, year={2009}, volume={50}, pages={123518} }

The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag–Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag–Leffler functions. Recent results associated with a generalized Langevin equation are recovered.

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#### References

SHOWING 1-10 OF 33 REFERENCES

Anomalous diffusion: exact solution of the generalized Langevin equation for harmonically bounded particle.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2006

69- PDF

Memory effects in the asymptotic diffusive behavior of a classical oscillator described by a generalized Langevin equation.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2008

28

Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2009

35- PDF

Anomalous diffusion induced by a Mittag-Leffler correlated noise.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2007

57- PDF

Generalized Langevin equation with fractional derivative and long-time correlation function.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2006

62

Generalized Langevin equations: Anomalous diffusion and probability distributions.

- Mathematics, Medicine
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

84- PDF

Fractional Langevin equation.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2001

342- PDF