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Acta Mechanica
Published in: Acta Mechanica 9/2021

28-06-2021 | Original Paper

Optimal control of the Cattaneo–Hristov heat diffusion model

Authors: Derya Avcı, Beyza Billur İskender Eroğlu

Published in: Acta Mechanica | Issue 9/2021

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Abstract

In this study, the optimal control problem for Cattaneo–Hristov heat diffusion, a partial differential equation including both fractional-order Caputo–Fabrizio and integer-order derivatives, is formulated for a rigid heat conductor with finite length. The state and control functions denoting temperature and heat source, respectively, are represented by eigenfunctions to eliminate the spatial coordinate. The necessary optimality conditions corresponding to a time-dependent dynamical system are derived via Hamilton’s principle. Because the optimality system contains both integer-order and fractional-order left- and right-side Caputo–Fabrizio derivatives, it cannot be solved analytically. Therefore, a numerical method based on the Volterra integral approach combined with the forward–backward finite difference schemes is applied to solve the system. Finally, the physical behaviours of the temperature state and heat control under the variation of the fractional parameter are depicted graphically.
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Metadata
Title
Optimal control of the Cattaneo–Hristov heat diffusion model
Authors
Derya Avcı
Beyza Billur İskender Eroğlu
Publication date
28-06-2021
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 9/2021
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-021-03019-z

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