Geodesic
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) no. 4, pp. 749-756.

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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.
Keywords: non-integer order system, heat transfer equation, infinite dimensional system, Feller semigroups
Mots-clés : układ niecałkowitego rzędu, wymiana ciepła, układ nieskończenie wymiarowy 
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Oprzędkiewicz, K.; Gawin, E.; Mitkowski, W. 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) no. 4, pp. 749-756. http://geodesic.mathdoc.fr/item/IJAMCS_2016_26_4_a1/

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