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Advances in Fractional Calculus pp 257–270Cite as

A Direct Approximation of Fractional Cole–Cole Systems by Ordinary First-order Processes

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Cole–Cole systems are widely used in electrochemistry to represent impedances of galvanic elements like fuel cells.

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References

  1. Cole KS, Cole RH (1941) Dispersion and absorption in dielectrics - I. Alternating current characteristics, J. Chem. Phys., 9(April):341-351.

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  2. Macdonald J (1987) Impedance Spectroscopy. Wiley, New York.

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  3. Haschka M, Rüger B, Krebs V (2004) Identification of the electrical behavior of a solid oxide fuel cell in the time-domain. Proceedings of Fractional Differentiation and its Applications 2004, Bordeaux, France., pp. 327-333.

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  4. Oustaloup A, Levron F, Nanot FM (2000) Frequency-band complex noninteger diff-erentiator: characterization and synthesis. IEEE Trans Circuits Syst., 47(January):25-39.

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  5. Fuoss RM, Kirkwood JG (1941) Electrical properties of solids. VIII. Dipole moments in polyvinyl chloride-diphenyl systems. J. Am. Chem. Soc., 63(April):385-394.

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Author information

Authors and Affiliations

  1. Institut für Regelungs- und Steuerungssysteme, Universität Karlsruhe (TH), Karlsruhe, Germany

    Markus Haschka & Volker Krebs

Authors
  1. Markus Haschka
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  2. Volker Krebs
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Editor information

Editors and Affiliations

  1. Université Bordeaux 1, – ENSEIRB, 351 cours de la Libération, F33405, Talence Cedex, France

    Jocelyn Sabatier

  2. Southern Illinois University, 62901, Carbondale, IL, USA

    Om Prakash Agrawal

  3. Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 4200-072, Porto, Portugal

    J. A. Tenreiro Machado

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© 2007 Springer

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Haschka, M., Krebs, V. (2007). A Direct Approximation of Fractional Cole–Cole Systems by Ordinary First-order Processes. In: Sabatier, J., Agrawal, O.P., Machado, J.A.T. (eds) Advances in Fractional Calculus. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6042-7_18

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  • DOI: https://doi.org/10.1007/978-1-4020-6042-7_18

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-6041-0

  • Online ISBN: 978-1-4020-6042-7

  • eBook Packages: EngineeringEngineering (R0)

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