TY  - JOUR
A1  - Sandev, Trifce
A1  - Metzler, Ralf
A1  - Tomovski, Zivorad
T1  - Velocity and displacement correlation functions for fractional generalized Langevin equations
T2  - Fractional calculus and applied analysis : an international journal for theory and applications
N2  - We study analytically a generalized fractional Langevin equation. General formulas for calculation of variances and the mean square displacement are derived. Cases with a three parameter Mittag-Leffler frictional memory kernel are considered. Exact results in terms of the Mittag-Leffler type functions for the relaxation functions, average velocity and average particle displacement are obtained. The mean square displacement and variances are investigated analytically. Asymptotic behaviors of the particle in the short and long time limit are found. The model considered in this paper may be used for modeling anomalous diffusive processes in complex media including phenomena similar to single file diffusion or possible generalizations thereof. We show the importance of the initial conditions on the anomalous diffusive behavior of the particle.
KW  - fractional generalized Langevin equation
KW  - frictional memory kernel
KW  - variances
KW  - mean square displacement
KW  - anomalous diffusion
Y1  - 2012
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/35689
SN  - 1311-0454
VL  - 15
IS  - 3
SP  - 426
EP  - 450
PB  - Versita
CY  - Warsaw
ER  -