# Time Fractional Cable Equation And Applications in Neurophysiology

## TL;DR

This paper extends the classical cable equation by incorporating a Caputo time fractional derivative, providing analytical solutions that model anomalous diffusion in neurophysiological structures like spiny dendrites.

## Contribution

It introduces a novel fractional derivative approach to the cable equation and derives analytical solutions using Laplace Transform, applicable to neurophysiology.

## Key findings

- Analytical solutions expressed with special functions
- Applicable to modeling anomalous diffusion in dendrites
- Solutions computed and visualized in Matlab

## 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.