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

  • Michał Sławomir WiraszkaEmail author
  • Piotr Sakrajda
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 559)


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.


Variable order model Diffusion Fractional calculus 



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


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Control and Industrial ElectronicsWarsaw University of TechnologyWarsawPoland

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