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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia


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1314-2224
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Volume 18, Issue 1

Issues

Electrolytic Fractional Derivative and Integral of Two-Terminal Element

Rashid Sh. Nigmatullin
  • Kazan Aviation Institute, Kazan, Russia
  • Kazan Aviation Institute, Kazan, Russia
  • Theoretical Physics Dept., Institute of Physics Kazan Federal University Kremlevskaya str.18, 420008, Kazan, RUSSIA
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/ Vladimir A. Belavin
  • Kazan Aviation Institute, Kazan, Russia
  • Kazan Aviation Institute, Kazan, Russia
  • Dept. of Radio-Electronic and Information & Measuring Technology Kazan National Research Technical University named after A. N. Tupolev Karl Marx str. 10, Kazan, RUSSIA
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Published Online: 2015-02-10 | DOI: https://doi.org/10.1515/fca-2015-0002

Abstract

To implement integration and differentiation of half-order, it is required a two-terminal element having the following impedance:

Z(jω)=1Aωe-jπ4.

For this purpose a chain-type RC-circuit [1] can be used. However a chaintype line comprising a large number of sections and requiring careful shielding against interferences is an expensive and massy device. In the present work, it is shown the possibility to use a small size electrolytic two-terminal element (hereinafter referred to as EEFD) to perform fractional differentiating and integrating.

MSC 2010: 01A60; 26A33; 94-03; 94CXX; 47N70

Key Words and Phrases: interpretation and implementation of fractional calculus operators; two-terminal element; impedance; RC-circuit

References

  • [1] E. F. Bazlov, R. Sh. Nigmatullin, Frequency characteristics of chain-type RC-circuit. Trudy KAI, Issue 73 (1963), In Russian.Google Scholar

  • [2] R. Sh. Nigmatullin, In: C. R. (Doklady) of the USSR Academy of Sciences 150, No 3 (1963), p. 600, In Russian.Web of ScienceGoogle Scholar

  • [3] A. N. Frumkin et al., Kinetics of Electrode Processes. Moscow State University, Moscow (1962), In Russian.Google Scholar

  • [4] P. Delahay, New Instruments and Methods in Electrochemistry. Moscow (1957), In Russian.Google Scholar

  • [5] I. M. Gelfand, G. E. Shilov, Generalized Functions and Operations with Them. Fizmatgiz, Moscow (1959), In Russian.Google Scholar

  • [6] R. Sh. Nigmatullin, V. A. Belavin, A. I. Miroshnikov, N. K. Lutskaia, Application of dedicated polarographic cell to fractional differentiating of I curves. Proceedings of the Second Polarographic Meeting (Abstracts), Kazan State University, Kazan (1962), In Russian.Google Scholar

About the article

Received: 1963-07-03

Published Online: 2015-02-10


Citation Information: Fractional Calculus and Applied Analysis, Volume 18, Issue 1, Pages 12–19, ISSN (Online) 1314-2224, DOI: https://doi.org/10.1515/fca-2015-0002.

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