Fractional differential equations in electrochemistry.

*(English)*Zbl 1177.78041Summary: Electrochemistry was one of the first sciences to benefit from the fractional calculus. Electrodes may be thought of as “transducers” of chemical fluxes into electricity. In a typical electrochemical cell, chemical species, such as ions or dissolved molecules, move towards the electrodes by diffusion. Likewise, other species are liberated into solution by the electrode reaction and diffuse away from the electrode into the bulk solution. It is demonstrated in this paper that the electric current is linearly related to the temporal semiderivative of the concentrations, at the electrode, of the species involved in the electrochemical reaction. More usefully, the semiintegral of the current provides immediate access information about concentrations.

##### MSC:

78A57 | Electrochemistry |

34A05 | Explicit solutions, first integrals of ordinary differential equations |

##### Keywords:

electrochemistry; diffusion; semiintegration; semidifferentiation; fractional-operators; electrodes; concentration; flux
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##### References:

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