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Crossover Dynamics from Superdiffusion to Subdiffusion: Models and Solutions

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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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  1. Department of Mathematics, Faculty of Education Alexandria University, Souter St., El-Shatby, P.O. Box 21526, Alexandria, Egypt

    Emad Awad

  2. Institute of Physics & Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476, Potsdam-Golm, Germany

    Ralf Metzler

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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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