Generalised fractional diffusion equations for subdiffusion on arbitrarily growing domains

C. N. Angstmann; B. I. Henry; A. V. McGann

doi:10.1103/physreve.96.042153

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arXiv · 1706.07168

Generalised fractional diffusion equations for subdiffusion on arbitrarily growing domains

C. N. Angstmann·B. I. Henry·A. V. McGann

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Abstract

Many physical phenomena occur on domains that grow in time. When the timescales of the phenomena and domain growth are comparable, models must include the dynamics of the domain. A widespread intrinsically slow transport process is subdiffusion. Many models of subdiffusion include a history dependence. This greatly confounds efforts to incorporate domain growth. Here we derive the fractional partial differential equations that govern subdiffusion on a growing domain, based on a Continuous Time Random Walk. This requires the introduction of a new, comoving, fractional derivative.

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C. N. Angstmann, B. I. Henry, A. V. McGann. 2017-07-13. Generalised fractional diffusion equations for subdiffusion on arbitrarily growing domains. https://doi.org/10.1103/physreve.96.042153

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