Abstract
Abstract In this article, the homotopy analysis method (HAM) is applied to solve the fractional cable equation by the Riemann-Liouville fractional partial derivative. This method includes an auxiliary parameter h which provides a convenient way of adjusting and controlling the convergence region of the series solution. In this study, approximate solutions of the fractional cable equation are obtained by HAM. We also give a convergence theorem for this equation. A suitable value for the auxiliary parameter h is determined and results obtained are presented by tables and figures.
Highlights
Fractional calculus has a very long history
We tried to find an approximate solution of this equation by homotopy analysis method (HAM), which is a semi-analytical method
It is not possible to find the analytical solutions of fractional partial differential equations in most cases
Summary
Fractional calculus has a very long history. this field lagged behind classic analysis. Fractional differential equations have been solved by many approximate methods. We will consider the cable equation that has been used in modeling the ion electro diffusion at the neurons. Studies were conducted on various biological and physical systems In this equation, the diffusion rate of species cannot be characterized by the single parameter of the diffusion constant [ ]. Henry et al derived a fractional cable equation from the fractional Nernst-Planck equations to model anomalous electrodiffusion of. They subsequently found a fractional cable equation by treating the neuron and its membrane as two separate materials governed by separate fractional Nernst-Planck equations. We will use the HAM, which is an approximate solution to solve this equation.
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