Time Fractional Cable Equation And Applications in Neurophysiology
arXiv:1702.05339 · doi:10.1016/j.chaos.2017.04.043
Abstract
We propose an extension of the cable equation by introducing a Caputo time fractional derivative. The fundamental solutions of the most common boundary problems are derived analitically via Laplace Transform, and result be written in terms of known special functions. This generalization could be useful to describe anomalous diffusion phenomena with leakage as signal conduction in spiny dendrites. The presented solutions are computed in Matlab and plotted.
10 figures. arXiv admin note: substantial text overlap with arXiv:1702.05325
References in corpus (5)
- Fractional Calculus: Integral and Differential Equations of Fractional Order
- Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics
- Characterizations and simulations of a class of stochastic processes to model anomalous diffusion
- Fractional kinetics emerging from ergodicity breaking in random media
- Fractional Cable Model for Signal Conduction in Spiny Neuronal Dendrites