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 analytically 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.
Vitali, S., Castellani, G., Mainardi, F. (2017). Time fractional cable equation and applications in neurophysiology. CHAOS, SOLITONS AND FRACTALS, 102, 467-472 [10.1016/j.chaos.2017.04.043].
Time fractional cable equation and applications in neurophysiology
Vitali, Silvia
Methodology
;Castellani, Gastone
Funding Acquisition
;Mainardi, Francesco
Supervision
2017
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 analytically 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.File | Dimensione | Formato | |
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