TY  - JOUR
A1  - Sandev, Trifce
A1  - Metzler, Ralf
A1  - Tomovski, Zivorad
T1  - Velocity and displacement correlation functions for fractional generalized Langevin equations
JF  - 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
U6  - https://doi.org/10.2478/s13540-012-0031-2
SN  - 1311-0454
VL  - 15
IS  - 3
SP  - 426
EP  - 450
PB  - Versita
CY  - Warsaw
ER  - 
TY  - JOUR
A1  - Sandev, Trifce
A1  - Tomovski, Zivorad
A1  - Dubbeldam, Johan L. A.
A1  - Chechkin, Aleksei V.
T1  - Generalized diffusion-wave equation with memory kernel
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We study generalized diffusion-wave equation in which the second order time derivative is replaced by an integro-differential operator. It yields time fractional and distributed order time fractional diffusion-wave equations as particular cases. We consider different memory kernels of the integro-differential operator, derive corresponding fundamental solutions, specify the conditions of their non-negativity and calculate the mean squared displacement for all cases. In particular, we introduce and study generalized diffusion-wave equations with a regularized Prabhakar derivative of single and distributed orders. The equations considered can be used for modeling the broad spectrum of anomalous diffusion processes and various transitions between different diffusion regimes.
KW  - diffusion-wave equation
KW  - Mittag-Leffler function
KW  - anomalous diffusion
Y1  - 2018
U6  - https://doi.org/10.1088/1751-8121/aaefa3
SN  - 1751-8113
SN  - 1751-8121
VL  - 52
IS  - 1
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -