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  -