The discrete, fractional order model of a two-dimensional temperature field using Grünwald-Letnikov definition

• Autorzy: Oprzędkiewicz Krzysztof

Identyfikatory

DOI

10.24425/bpasts.2024.150332

• Języki publikacji: EN

Abstrakty

EN

In the paper a new, fractional order, discrete model of a two-dimensional temperature field is addressed. The proposed model uses Grünwald-Letnikov definition of the fractional operator. Such a model has not been proposed yet. Elementary properties of the model: practical stability, accuracy and convergence are analysed. Analytical conditions of stability and convergence are proposed and they allow to estimate the orders of the model. Theoretical considerations are validated using exprimental data obtained with the use of a thermal imaging camera. Results of analysis supported by experiments point that the proposed model assures good accuracy and convergence for low order and relatively short memory length.

Słowa kluczowe

EN

fractional order systems; heat transfer equation; fractional order state equation; practical stability; accuracy; convergence; thermal camera; Grünwald–Letnikov definition

PL

układy ułamkowego rzędu; równanie wymiany ciepła; stabilność praktyczna; dokładność; zbieżność; kamera termowizyjna; definicja Grünwalda-Letnikowa; równanie stanu rzędu ułamkowego

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2024
• Tom: Vol. 72, nr 4
• Strony: art. no. e150332
• Opis fizyczny: Bibliogr. 36 poz., rys., tab.

Twórcy

autor

Oprzędkiewicz Krzysztof

• AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Kraków, Poland

• https://orcid.org/0000-0002-8162-0011

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