Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions.

@article{Langlands2009FractionalCE,
  title={Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions.},
  author={T. A. M. Langlands and Bruce Ian Henry and Susan L. Wearne},
  journal={Journal of mathematical biology},
  year={2009},
  volume={59 6},
  pages={761-808}
}
We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with… CONTINUE READING

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