Details

Title

Fractional discrete-continuous model of heat transfer process

Journal title

Archives of Control Sciences

Yearbook

2021

Volume

vol. 31

Issue

No 2

Authors

Affiliation

Oprzędkiewicz, Krzysztof : AGH University of Science and Technology in Krakow, Faculty of Electrical Engineering, Automatics, Computer Science and Robotics, Department of Automatics and Biomedical Engineering, Kraków, Poland ; Dziedzic, Klaudia : AGH University of Science and Technology in Krakow, Faculty of Electrical Engineering, Automatics, Computer Science and Robotics, Department of Automatics and Biomedical Engineering, Kraków, Poland

Keywords

non integer order systems ; heat transfer equation ; finite difference ; Caputo operator ; positive systems

Divisions of PAS

Nauki Techniczne

Coverage

287-306

Publisher

Committee of Automatic Control and Robotics PAS

Bibliography

[1] R. Almeida and D.F.M. Torres: Necessary and sufficient conditions for the fractional calculus of variations with caputo derivatives. Communications in Nonlinear Science and Numerical Simulation, 16(3), (2011), 1490–1500, DOI: 10.1016/j.cnsns.2010.07.016.
[2] A. Atangana and D. Baleanu: New fractional derivatives with non-local and non-singular kernel: theory and application to heat transfer. Thermal Sciences, 20(2), (2016), 763–769, DOI: 10.2298/TSCI160111018A.
[3] R. Caponetto, G. Dongola, L. Fortuna, and I. Petras: Fractional order systems: Modeling and Control Applications. In: Leon O. Chua, editor, World Scientific Series on Nonlinear Science, pages 1–178. University of California, Berkeley, 2010.
[4] S. Das: Functional Fractional Calculus for System Identyfication and Control. Springer, Berlin, 2010.
[5] M. Dlugosz and P. Skruch: The application of fractional-order models for thermal process modelling inside buildings. Journal of Building Physics, 39(5), (2016), 440–451, DOI: 10.1177/1744259115591251.
[6] A. Dzielinski, D. Sierociuk, and G. Sarwas: Some applications of fractional order calculus. Bulletin of the Polish Academy of Sciences, Technical Sciences, 58(4), (2010), 583–592, DOI: 10.2478/v10175-010-0059-6.
[7] C.G. Gal and M. Warma Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions. Evolution Equations and Control Theory, 5(1), (2016), 61–103, DOI: 10.3934/eect.2016.5.61.
[8] T. Kaczorek Fractional positive contiuous-time linear systems and their reachability. International Journal of Applied Mathematics and Computer Science, 18(2), (2008), 223–228, DOI: 10.2478/v10006-008-0020-0.
[9] T. Kaczorek: Singular fractional linear systems and electrical circuits. International Journal of Applied Mathematics and Computer Science, 21(2), (2011), 379–384, DOI: 10.2478/v10006-011-0028-8.
[10] T. Kaczorek and K. Rogowski: Fractional Linear Systems and Electrical Circuits. Bialystok University of Technology, Bialystok, 2014.
[11] A. Kochubei: Fractional-parabolic systems, preprint, arxiv:1009.4996 [math.ap], 2011.
[12] W. Mitkowski: Approximation of fractional diffusion-wave equation. Acta Mechanica et Automatica, 5(2), (2011), 65–68.
[13] W. Mitkowski: Finite-dimensional approximations of distributed rc networks. Bulletin of the Polish Academy of Sciences. Technical Sciences, 62(2), (2014), 263–269, DOI: 10.2478/bpasts-2014-0026.
[14] W. Mitkowski,W. Bauer, and M. Zagorowska: Rc-ladder networks with supercapacitors. Archives of Electrical Engineering, 67(2), (2018), 377– 389, DOI: 10.24425/119647.
[15] K. Oprzedkiewicz: The discrete-continuous model of heat plant. Automatyka, 2(1), (1998), 35–45 (in Polish).
[16] K. Oprzedkiewicz: The interval parabolic system. Archives of Control Sciences, 13(4), (2003), 415–430.
[17] K. Oprzedkiewicz:Acontrollability problem for a class of uncertain parameters linear dynamic systems. Archives of Control Sciences, 14(1), (2004), 85–100.
[18] K. Oprzedkiewicz: An observability problem for a class of uncertainparameter linear dynamic systems. International Journal of Applied Mathematics and Computer Science, 15(3), (2005), 331–338.
[19] K. Oprzedkiewicz:Non integer order, state space model of heat transfer process using Caputo-Fabrizio operator. Bulletin of the Polish Academy of Sciences. Technical Sciences, 66(3), (2018), 249–255, DOI: 10.24425/122105.
[20] K. Oprzedkiewicz: Non integer order, state space model of heat transfer process using Atangana-Baleanu operator. Bulletin of the Polish Academy of Sciences. Technical Sciences, 68(1), (2020), 43–50, DOI: 10.24425/bpasts.2020.131828.
[21] K. Oprzedkiewicz: Positivity problem for the one dimensional heat transfer process. ISA Transactions, 112, (2021), 281-291 DOI: .
[22] K. Oprzedkiewicz: Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator. Bulletin of the Polish Academy of Sciences. Technical Sciences, 69(1), (2021), 1–10, DOI: 10.24425/bpasts.2021.135843.
[23] K. Oprzedkiewicz, K. Dziedzic, and Ł. Wi˛ eckowski: Non integer order, discrete, state space model of heat transfer process using Grünwald-Letnikov operator. Bulletin of the Polish Academy of Sciences. Technical Sciences, 67(5), (2019), 905–914, DOI: 10.24425/bpasts.2019.130873.
[24] K. Oprzedkiewicz and E. Gawin: A non-integer order, state space model for one dimensional heat transfer process. Archives of Control Sciences, 26(2), (2016), 261–275, DOI: 10.1515/acsc-2016-0015.
[25] K. Oprzedkiewicz, E. Gawin, and W. Mitkowski: Modeling heat distribution with the use of a non-integer order, state space model. International Journal of Applied Mathematics and Computer Science, 26(4), (2016), 749– 756, DOI: 10.1515/amcs-2016-0052.
[26] K. Oprzedkiewicz and W. Mitkowski: A memory-efficient nonintegerorder discrete-time state-space model of a heat transfer process. International Journal of Applied Mathematics and Computer Science, 28(4), (2018), 649–659, DOI: 10.2478/amcs-2018-0050.
[27] K. Oprzedkiewicz,W. Mitkowski, E.Gawin, and K. Dziedzic: The Caputo vs. Caputo-Fabrizio operators in modeling of heat transfer process. Bulletin of the Polish Academy of Sciences. Technical Sciences, 66(4), (2018), 501– 507, DOI: 10.24425/124267.
[28] K. Oprzedkiewicz, E. Gawin, and W. Mitkowski: Parameter identification for non integer order, state space models of heat plant. In MMAR 2016: 21th international conference on Methods and Models in Automation and Robotics: 29 August–01 September 2016, Międzyzdroje, Poland, pages 184– 188, 2016.
[29] P. Ostalczyk: Discrete Fractional Calculus. Applications in Control and Image Processing. Worlsd Scientific Publishing, Singapore, 2016.
[30] I. Podlubny: Fractional Differential Equations. Academic Press, San Diego, 1999.
[31] G. Recktenwald: Finite-difference approximations to the heat equation. 2011.
[32] M. Rozanski: Determinants of two kinds of matrices whose elements involve sine functions. Open Mathematics, 17(1), (2019), 1332–1339, DOI: 10.1515/math-2019-0096.
[33] N. Al Salti, E. Karimov, and S. Kerbal: Boundary-value problems for fractional heat equation involving caputo-fabrizio derivative. New Trends in Mathematical Sciences, 4(4), (2016), 79–89, arXiv:1603.09471.
[34] D. Sierociuk, T. Skovranek, M. Macias, I. Podlubny, I. Petras, A. Dzielinski, and P. Ziubinski: Diffusion process modeling by using fractional-order models. Applied Mathematics and Computation, 257(1), (2015), 2–11, DOI: 10.1016/j.amc.2014.11.028.

Date

2021.07.01

Type

Article

Identifier

DOI: 10.24425/acs.2021.137419
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