Fractional diffusion equation and impedance spectroscopy of electrolytic cells.

Anomalous diffusion and memory effects on the impedance spectroscopy for finite-length situations.

The contribution of ions to the electrical impedance of an electrolytic cell limited by perfect blocking electrodes is determined by considering the role of the anomalous diffusion process and memory effects. Analytical solutions for fractional diffusion equations together with Poisson's equation relating the effective electric field to the net charge density are found. This procedure allows th...

Anomalous diffusion governed by a fractional diffusion equation and the electrical response of an electrolytic cell.

The electrical response of an electrolytic cell in which the diffusion of mobile ions in the bulk is governed by a fractional diffusion equation of distributed order is analyzed. The boundary conditions at the electrodes limiting the sample are described by an integro-differential equation governing the kinetic at the interface. The analysis is carried out by supposing that the positive and neg...

A New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

Significance of small voltage in impedance spectroscopy measurements on electrolytic cells

Finite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients

In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integ...