Time fractional cable equation and applications in neurophysiology

DOI10.1016/j.chaos.2017.04.043zbMath1374.92025arXiv1702.05339OpenAlexW2608403831MaRDI QIDQ1677801

Gastone Castellani, Silvia Vitali, Francesco Mainardi

Publication date: 13 November 2017

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.05339

zbMATH Keywords

Laplace transformdendritessubdiffusionfractional cable equationWright functionsEfros theorem

Mathematics Subject Classification ID

Neural biology (92C20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Physiology (general) (92C30) Fractional partial differential equations (35R11)

Related Items (12)

A priori bounds of the solution of a one point IBVP for a singular fractional evolution equation ⋮ Time-fractional diffusion with mass absorption under harmonic impact ⋮ Non-local telegrapher's equation as a transmission line model ⋮ Finite difference/spectral methods for the two-dimensional distributed-order time-fractional cable equation ⋮ Fractional bosonic strings ⋮ Numerical investigation of the time-fractional Black-Scholes equation with barrier choice of regulating European option ⋮ Fractional heat conduction with heat absorption in a sphere under Dirichlet boundary condition ⋮ The impact of the Chebyshev collocation method on solutions of the time-fractional Black-Scholes ⋮ Time-Fractional Heat Conduction with Heat Absorption in a Half-Line Domain Due to Boundary Value of the Heat Flux Varying Harmonically in Time ⋮ Numerical analysis of time fractional Black-Scholes European option pricing model arising in financial market ⋮ Fractional cable problem in the frame of meshless singular boundary method ⋮ Dispersion relations for the time-fractional Cattaneo-Maxwell heat equation

Uses Software

• Matlab
• LaplaceAndzTransform

Cites Work

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• The M-Wright function as a generalization of the Gaussian density for fractional diffusion processes
• A Unified Framework for Numerically Inverting Laplace Transforms
• Fractional Cable Equation Models for Anomalous Electrodiffusion in Nerve Cells: Finite Domain Solutions
• Characterizations and simulations of a class of stochastic processes to model anomalous diffusion
• Fractional Calculus: Integral and Differential Equations of Fractional Order

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