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Fractal Fract 2018, 2(1), 6; https://doi.org/10.3390/fractalfract2010006

Emergence of Fractional Kinetics in Spiny Dendrites

Dipartimento di Fisica e Astronomia, Università di Bologna, Viale Berti Pichat 6, 40127 Bologna, Italy
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Received: 21 December 2017 / Revised: 22 January 2018 / Accepted: 22 January 2018 / Published: 25 January 2018
(This article belongs to the Special Issue Fractional Dynamics)
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Abstract

Fractional extensions of the cable equation have been proposed in the literature to describe transmembrane potential in spiny dendrites. The anomalous behavior has been related in the literature to the geometrical properties of the system, in particular, the density of spines, by experiments, computer simulations, and in comb-like models. The same PDE can be related to more than one stochastic process leading to anomalous diffusion behavior. The time-fractional diffusion equation can be associated to a continuous time random walk (CTRW) with power-law waiting time probability or to a special case of the Erdély-Kober fractional diffusion, described by the ggBm. In this work, we show that time fractional generalization of the cable equation arises naturally in the CTRW by considering a superposition of Markovian processes and in a ggBm-like construction of the random variable. View Full-Text
Keywords: fractional calculus; generalized grey Brownian motion; continuous time random walk; dendrites; neurons; cable equation fractional calculus; generalized grey Brownian motion; continuous time random walk; dendrites; neurons; cable equation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Vitali, S.; Mainardi, F.; Castellani, G. Emergence of Fractional Kinetics in Spiny Dendrites. Fractal Fract 2018, 2, 6.

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