TY  - JOUR
A1  - Sandev, Trifce
A1  - Metzler, Ralf
A1  - Chechkin, Aleksei V.
T1  - From continuous time random walks to the generalized diffusion equation
JF  - Fractional calculus and applied analysis : an international journal for theory and applications
N2  - We obtain a generalized diffusion equation in modified or Riemann-Liouville form from continuous time random walk theory. The waiting time probability density function and mean squared displacement for different forms of the equation are explicitly calculated. We show examples of generalized diffusion equations in normal or Caputo form that encode the same probability distribution functions as those obtained from the generalized diffusion equation in modified form. The obtained equations are general and many known fractional diffusion equations are included as special cases.
KW  - continuous time random walk (CTRW)
KW  - generalized diffusion equation
KW  - Mittag-Leffler functions
KW  - anomalous diffusion
Y1  - 2018
U6  - https://doi.org/10.1515/fca-2018-0002
SN  - 1311-0454
SN  - 1314-2224
VL  - 21
IS  - 1
SP  - 10
EP  - 28
PB  - De Gruyter
CY  - Berlin
ER  -