Fractional Langevin equation and Riemann-Liouville fractional derivative
Departamento de Fısica, Universidade Estadual de Maringá, Av. Colombo 5790, 87020-900, Maringá, PR, Brazil
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Accepted: 3 September 2007
Published online: 22 October 2007
In this present work we consider a fractional Langevin equation with Riemann-Liouville fractional time derivative which modifies the classical Newtonian force, nonlocal dissipative force, and long-time correlation. We investigate the first two moments, variances and position and velocity correlation functions of this system. We also compare them with the results obtained from the same fractional Langevin equation which uses the Caputo fractional derivative.
PACS: 02.50.Ey Stochastic processes – / 05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.) – / 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion –
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2007