TY  - JOUR
A1  - Awad, Emad
A1  - Metzler, Ralf
T1  - Crossover dynamics from superdiffusion to subdiffusion
BT  - models and solutions
JF  - Fractional calculus and applied analysis : an international journal for theory and applications
N2  - The Cattaneo or telegrapher's equation describes the crossover from initial ballistic to normal diffusion. Here we study and survey time-fractional generalisations of this equation that are shown to produce the crossover of the mean squared displacement from superdiffusion to subdiffusion. Conditional solutions are derived in terms of Fox H-functions and the dth-order moments as well as the diffusive flux of the different models are derived. Moreover, the concept of the distribution-like is proposed as an alternative to the probability density function.
KW  - Cattaneo equation
KW  - telegrapher's equation
KW  - crossover dynamics
KW  - fractional dynamic equations
KW  - anomalous diffusion
KW  - superdiffusion and
KW  - subdiffusion
KW  - Fox H-functions
Y1  - 2020
U6  - https://doi.org/10.1515/fca-2020-0003
SN  - 1311-0454
SN  - 1314-2224
VL  - 23
IS  - 1
SP  - 55
EP  - 102
PB  - De Gruyter
CY  - Berlin ; Boston
ER  -