Abstract
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 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.
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Awad, E., Metzler, R. Crossover Dynamics from Superdiffusion to Subdiffusion: Models and Solutions. Fract Calc Appl Anal 23, 55–102 (2020). https://doi.org/10.1515/fca-2020-0003
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DOI: https://doi.org/10.1515/fca-2020-0003