TY - JOUR

T1 - Generalized diffusion-wave equation with memory kernel

AU - Sandev, Trifce

AU - Tomovski, Zhivorad

AU - Dubbeldam, Johan L.A.

AU - Chechkin, Aleksei

PY - 2019

Y1 - 2019

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.

AB - 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 - anomalous diffusion

KW - diffusion-wave equation

KW - Mittag-Leffler function

UR - http://www.scopus.com/inward/record.url?scp=85057713983&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/aaefa3

DO - 10.1088/1751-8121/aaefa3

M3 - Article

AN - SCOPUS:85057713983

VL - 52

SP - 1

EP - 23

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

M1 - 015201

ER -