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