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Switching Energy Loss in Fractional-Order Time-Varying Heat Diffusion Model

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Advances in Non-Integer Order Calculus and Its Applications (RRNR 2018)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 559))

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Abstract

Anomalous heat diffusion process is one of the most popular examples of real world fractional-order system modelling. It has been shown, that such approach is well suited for modelling diffusion in fractal, porous media. A number of papers examining this problem have been published, either for constant- or variable-order systems. However, few of them addressed energy-related issues of such process. Better understanding of the relationship between the energy and order would have a great impact on fractional order modelling, helping to predict the results of stochastic processes in varying, complicated systems and making it easier to find the real order of the system.

In this paper a relationship between switching orders and integral energy loss of the system is being investigated.

Two-dimensional time-varying numerical model and its simulation based on finite element method is being considered in order to provide consistent data for further real-case experiments.

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Acknowledgment

This work was supported by the Polish National Science Center with the decision number UMO-2014/15/B/ST7/00480.

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Authors and Affiliations

  1. Institute of Control and Industrial Electronics, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland

    Michał Sławomir Wiraszka & Piotr Sakrajda

Authors
  1. Michał Sławomir Wiraszka
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  2. Piotr Sakrajda
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Corresponding author

Correspondence to Michał Sławomir Wiraszka .

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Editors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Agnieszka B. Malinowska

  2. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Dorota Mozyrska

  3. Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland

    Łukasz Sajewski

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Wiraszka, M.S., Sakrajda, P. (2020). Switching Energy Loss in Fractional-Order Time-Varying Heat Diffusion Model. In: Malinowska, A., Mozyrska, D., Sajewski, Ł. (eds) Advances in Non-Integer Order Calculus and Its Applications. RRNR 2018. Lecture Notes in Electrical Engineering, vol 559. Springer, Cham. https://doi.org/10.1007/978-3-030-17344-9_22

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