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Fractional differential equations in electrochemistry. (English) Zbl 1177.78041
Summary: 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.

78A57 Electrochemistry
34A05 Explicit solutions, first integrals of ordinary differential equations
Full Text: DOI
[1] Von Leibniz, G. W.: Leibnizen mathematische schriften, Leibnizen mathematische schriften 2 (1962)
[2] Gemant, A.: A method of analyzing experimental results obtained from elasto-viscous bodies, Physics (New York) 7, 311 (1936)
[3] Blair, G. W. Scott: The role of psychophysics in rheology, J colloid sci 2, 21 (1947)
[4] Blair, G. W. Scott; Veinoglou, B. C.; Caffeyn, J. E.: Limitations of the Newtonian time scale in relation to non-equilibrium rheological states and a theory of quasi-properties, Proc royal soc ser A 187, 69 (1947) · Zbl 0029.08602 · doi:10.1098/rspa.1947.0029
[5] Blair, G. W. Scott; Caffeyn, J. E.: An application of the theory of quasi-properties to the treatment of stress – strain relations, Philos mag 40, 80 (1949) · Zbl 0035.41501
[6] Blair, W. Scott: Some aspects of the search for invariants, Brit J philos sci 1, 230 (1950)
[7] Meyer RF. A heat-flux meter for use with thin film surface thermometers. Aeronautical report LR-279, National Research Council of Canada, Ottawa; 1960.
[8] Oldham, K. B.; Myland, J. C.: Fundamentals of electrochemical science, (1994)
[9] Oldham, K. B.; Zoski, C. G.: Mass transport to electrodes, Electrode kinetics: principles and methodology 26, 95 (1986)
[10] Delahay, P.: New instrumental methods in electrochemistry, (1954)
[11] Oldham, K. B.; Spanier, J.: The fractional calculus, (1974) · Zbl 0292.26011
[12] Oldham, K. B.: A new approach to the solution of electrochemical problems involving diffusion, Anal chem 41, 1904 (1969)
[13] Oldham, K. B.; Spanier, J.: The replacement of fick’s laws by a formulation involving semidifferentiation, J electroanal chem interf electrochem 26, 331 (1970)
[14] Oldham, K. B.: A signal-independent electroanalytical method, Anal chem 44, 196 (1972)
[15] Oldham, K. B.: Tables of semiintegrals, J electroanal chem 430, 1 (1997)
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