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Fractional Calculus as a Simple Tool for Modeling and Analysis of Long Memory Process in Industry

Author

Listed:
  • Ivo Petráš

    (Faculty of BERG, Technical University of Košice, Němcovej 3, 04200 Košice, Slovakia)

  • Ján Terpák

    (Faculty of BERG, Technical University of Košice, Němcovej 3, 04200 Košice, Slovakia)

Abstract

This paper deals with the application of the fractional calculus as a tool for mathematical modeling and analysis of real processes, so called fractional-order processes. It is well-known that most real industrial processes are fractional-order ones. The main purpose of the article is to demonstrate a simple and effective method for the treatment of the output of fractional processes in the form of time series. The proposed method is based on fractional-order differentiation/integration using the Grünwald–Letnikov definition of the fractional-order operators. With this simple approach, we observe important properties in the time series and make decisions in real process control. Finally, an illustrative example for a real data set from a steelmaking process is presented.

Suggested Citation

  • Ivo Petráš & Ján Terpák, 2019. "Fractional Calculus as a Simple Tool for Modeling and Analysis of Long Memory Process in Industry," Mathematics, MDPI, vol. 7(6), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:511-:d:237258
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    References listed on IDEAS

    as
    1. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Economic Growth Model with Constant Pace and Dynamic Memory," Papers 1701.06299, arXiv.org, revised Apr 2019.
    2. Ming Li, 2010. "Fractal Time Series—A Tutorial Review," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-26, December.
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