Accuracy estimation of the approximated Atangana-Baleanu operator

• Autorzy: Oprzędkiewicz Krzysztof , Mitkowski Wojciech

Identyfikatory

DOI

10.17512/jamcm.2019.4.05

• Języki publikacji: EN

Abstrakty

EN

In the paper, the accuracy analysis of the approximation of the Atangana-Baleanu (AB) operator is presented. The AB operator is the nonsingular kernel operator proposed by Atangana and Baleanu. It is obtained by replacing the exponential function in the Caputo-Fabrizio operator by the Mittag-Leffler function. The Laplace transform of the AB operator requires approximating the factor sa. This is done using the well-known Oustaloup Recursive Approximaion (ORA) approximation. The step and frequency responses of the approximation are compared to the analytical responses. As the cost function, the FIT function available in MATLAB was applied. Results of simulations show that the use of ORA allows us to obtain the accurate approximant of the AB operator.

Słowa kluczowe

EN

Caputo operator; Mittag-Leffler function; ORA approximation

PL

aproksymacja ORA; funkcja Mittag-Lefflera

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2019
• Tom: Vol. 18, nr 4
• Strony: 53--62
• Opis fizyczny: Bibliogr. 10 poz., rys., tab.

Twórcy

autor

Oprzędkiewicz Krzysztof

• Department of Automatics and Robotics, AGH University Krakow, Poland

autor

Mitkowski Wojciech

• Department of Automatics and Robotics, AGH University Krakow, Poland

Bibliografia

• [1] Atangana, A., & Baleanu, D. (2016). New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Thermal Science, 20, 2, 763-769.
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• [3] Sene, N. (2019). Analytical solutions of Hristov diffusion equations with non-singular fractional derivatives. Chaos 29, 023112; https://doi.org/10.1063/1.5082645.
• [4] Gomez, J.F., Torres, L., & Escobar, R.F. (2019). Fractional Derivatives with Mittag-Leffler Kernel Trends and Applications in Science and Engineering. Studies in Systems, Decision and Control, vol. 194, Springer.
• [5] Oprzedkiewicz, K. (2016). Accuracy estimation of digital fractional order PID controller. Theory and applications of non-integer order systems. 8th Conference on Non-integer order calculus and its applications: [20-21 September 2016], Zakopane, Poland. Eds. A. Babiarz et al. Springer International Publishing, cop. 2017 (Lecture Notes in Electrical Engineering; ISSN 1876-1100; vol. 407), ISBN: 978-3-319-45473-3; e-ISBN: 978-3-319-45474-0, pp. 265-275.
• [6] Oprzedkiewicz, K., Mitkowski,W., & Gawin, E. (2016). An estimation of accuracy of Oustaloup approximation. Challenges in automation, robotics and measurement techniques: proceedings of AUTOMATION-2016, March 2-4, 2016, Warsaw, Poland. Eds. R. Szewczyk, C. Zieliński, M. Kaliczyńska. Springer International Publishing, cop. 2016. (Advances in Intelligent Systems and Computing; ISSN 2194-5357; vol. 440), ISBN: 978-3-319-29356-1; e-ISBN: 978-3-319-29357-8, pp. 299-307.
• [7] Kaczorek, T. (2011). Selected Problems in Fractional Systems Theory. Springer Verlag.
• [8] Kaczorek, T., & Rogowski, K. (2014). Fractional Linear Systems and Electrical Circuits. Bialystok University of Technology.
• [9] Oustaloup, A., Levron, F., Mathieu, B., & Nanot, F.M. (2000). Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Transactions on Circuits and Systems I: Fundamental Theory Applications, 47, 1, 25-39.
• [10] Caponetto, R., Dongola, G., Fortuna, l., & Petras, I. (2010), Fractional Order Systems. Modeling and Control Applications. World Scientific Series on Nonlinear Science, Series A, vol. 72, World Scientific Publishing.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).