A new, state space, non-integer order model for the heat transfer process is presented. The proposed model is based on a Feller semigroup one, the derivative with respect to time is expressed by the non-integer order Caputo operator, and the derivative with respect to length is described by the non-integer order Riesz operator. Elementary properties of the state operator are proven and a formula for the step response of the system is also given. The proposed model is applied to the modeling of temperature distribution in a one dimensional plant. Results of experiments show that the proposed model is more accurate than the analogical integer order model in the sense of the MSE cost function.
@article{bwmeta1.element.bwnjournal-article-amcv26i4p749bwm,
author = {Krzysztof Oprz\k edkiewicz and Edyta Gawin and Wojciech Mitkowski},
title = {Modeling heat distribution with the use of a non-integer order, state space model},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {26},
year = {2016},
pages = {749-756},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv26i4p749bwm}
}
Krzysztof Oprzędkiewicz; Edyta Gawin; Wojciech Mitkowski. Modeling heat distribution with the use of a non-integer order, state space model. International Journal of Applied Mathematics and Computer Science, Tome 26 (2016) pp. 749-756. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv26i4p749bwm/
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