Emergence of Fractional Kinetics in Spiny Dendrites
AbstractFractional 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
Share & Cite This Article
Vitali, S.; Mainardi, F.; Castellani, G. Emergence of Fractional Kinetics in Spiny Dendrites. Fractal Fract 2018, 2, 6.
Vitali S, Mainardi F, Castellani G. Emergence of Fractional Kinetics in Spiny Dendrites. Fractal and Fractional. 2018; 2(1):6.Chicago/Turabian Style
Vitali, Silvia; Mainardi, Francesco; Castellani, Gastone. 2018. "Emergence of Fractional Kinetics in Spiny Dendrites." Fractal Fract 2, no. 1: 6.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.