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Time fractional cable equation and applications in neurophysiology

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  • Vitali, Silvia
  • Castellani, Gastone
  • Mainardi, Francesco

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.

Suggested Citation

  • Vitali, Silvia & Castellani, Gastone & Mainardi, Francesco, 2017. "Time fractional cable equation and applications in neurophysiology," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 467-472.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:467-472
    DOI: 10.1016/j.chaos.2017.04.043
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    References listed on IDEAS

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    1. Joseph Abate & Ward Whitt, 2006. "A Unified Framework for Numerically Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 408-421, November.
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    Cited by:

    1. Cvetićanin, Stevan M. & Zorica, Dušan & Rapaić, Milan R., 2021. "Non-local telegrapher’s equation as a transmission line model," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    2. Bohdan Datsko & Igor Podlubny & Yuriy Povstenko, 2019. "Time-Fractional Diffusion-Wave Equation with Mass Absorption in a Sphere under Harmonic Impact," Mathematics, MDPI, vol. 7(5), pages 1-11, May.

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