We use two different hyperbolic subdiffusion equations with fractional time derivatives (the generalized Cattaneo equations) to study the transport process of electrolytes in media where subdiffusion occurs. In these models the flux is delayed in a non-zero time with respect to the concentration gradient. In particular, we obtain the formulae of electrochemical subdiffusive impedance of a spatially limited sample in the limit of large and small pulsation of the electric field. The boundary conditions at the external wall of the sample are taken in the general form as a linear combination of the subdiffusive flux and the concentration of transported particles. We also discuss the influence of the equation parameters (the subdiffusion parameter and the delay time) on the Nyquist impedance plots.
Using the quasistatic approximation we show that in a subdiffusion-reaction system with arbitrary non-zero values of subdiffusion coefficients, the reaction front x f (t) evolves in time according to the formula x f (t) = Kt α/2 , with α being the subdiffusion parameter and K which is controlled by the subdiffusion coefficients. The parameter K is determined by the equation derived in this paper. To check correctness of our analysis, we compare analytical functions derived in this paper with the results obtained numerically for the subdiffusion-reaction equations.
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Using the quasistatic approximation, we show that in a subdiffusion-reaction system with arbitrary nonzero values of subdiffusion coefficients, the reaction front x_{f}(t) evolves in time as x_{f}(t)=Kt;{alpha2} , with alpha being the subdiffusion parameter and K being controlled by the subdiffusion coefficients. To check the correctness of our analysis, we compare approximate analytical solutions of the subdiffusion-reaction equations with the numerical ones.
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