Crossover dynamics from superdiffusion to subdiffusion: Models and solutions
2020 ◽
Vol 23
(1)
◽
pp. 55-102
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Keyword(s):
AbstractThe 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 δth-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.
2017 ◽
Vol 3
(3)
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Keyword(s):
2007 ◽
Vol 464
(2091)
◽
pp. 555-572
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1993 ◽
Vol 43
(1-2)
◽
pp. 13-24