In the present work, the numerical solution of two-dimensional variable-order fractional cable (VOFC) equation using meshless collocation methods with thin plate spline radial basis functions is considered. In the proposed methods, we first use two schemes of order O(τ2) for the time derivatives and then meshless approach is applied to the space component. Numerical results obtained ...

The Cable equation has been one of the most fundamental equations for modeling neuronal dynamics. In this paper, we consider the numerical solution of the fractional Cable equation, which is a generalization of the classical Cable equation by taking into account the anomalous diffusion in the movement of the ions in neuronal system. A schema combining a finite difference approach in the time di...

We consider the fractional cable equation. For solution of fractional Cable equation involving Caputo fractional derivative, a new difference scheme is constructed based on Crank Nicholson difference scheme. We prove that the proposed method is unconditionally stable by using spectral stability technique.

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases....

In this paper, a variable-order nonlinear cable equation is considered. The numerical method with first order temporal accuracy and fourth order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second order temporal accuracy and fourth order spatial accuracy. Finally, the resul...

The Riccati differential equation with a fractional derivative of variable order is considered. A in the original implies hereditary property medium, i.e., dependence current state dynamic system on its previous states. software called Numerical Solution Fractional-Differential Equation (briefly NSFDRE) created; it allows one to compute numerical solution Cauchy problem for order. algorithm imp...