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

Ivo Petráš and Ján Terpák
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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

Mathematics, 2019, vol. 7, issue 6, 1-9

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.

Keywords: fractional calculus; fractional-order system; long memory; time series; Hurst exponent (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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