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Volume 20, Issue 3
A Fractional-Order Alternative for Phase-Lagging Equation

Cui-Cui Ji, Weizhong Dai & Ronald E. Mickens

DOI: 10.4208/ijnam2023-1016

Int. J. Numer. Anal. Mod., 20 (2023), pp. 391-406.

Published online: 2023-03

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  • Abstract

Phase-lagging equation (PLE) is an equation describing micro/nano scale heat conduction, where the lagging response must be included, particularly under low temperature or high heat-flux conditions. However, finding the analytical or numerical solutions of the PLE is tedious in general. This article aims at seeking a fractional-order heat equation that is a good alternative for the PLE. To this end, we consider the PLE with simple initial and boundary conditions and obtain a fractional-order heat equation and an associated numerical method for approximating the solution of the PLE. In order to better approximate the PLE, the Levenberg-Marquardt iterative method is employed to estimate the optimal parameters in the fractional-order heat equation. This fractional-order alternative is then tested and compared with the PLE. Results show that the fractional method is promising.

  • Keywords

Phase-lagging equation, fractional-order heat equation, numerical scheme, parameter estimation.

  • AMS Subject Headings

35A35, 65M06, 65M12, 65M32

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-20-391, author = {Ji , Cui-CuiDai , Weizhong and Mickens , Ronald E.}, title = {A Fractional-Order Alternative for Phase-Lagging Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2023}, volume = {20}, number = {3}, pages = {391--406}, abstract = {

Phase-lagging equation (PLE) is an equation describing micro/nano scale heat conduction, where the lagging response must be included, particularly under low temperature or high heat-flux conditions. However, finding the analytical or numerical solutions of the PLE is tedious in general. This article aims at seeking a fractional-order heat equation that is a good alternative for the PLE. To this end, we consider the PLE with simple initial and boundary conditions and obtain a fractional-order heat equation and an associated numerical method for approximating the solution of the PLE. In order to better approximate the PLE, the Levenberg-Marquardt iterative method is employed to estimate the optimal parameters in the fractional-order heat equation. This fractional-order alternative is then tested and compared with the PLE. Results show that the fractional method is promising.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2023-1016}, url = {http://global-sci.org/intro/article_detail/ijnam/21539.html} }
TY - JOUR T1 - A Fractional-Order Alternative for Phase-Lagging Equation AU - Ji , Cui-Cui AU - Dai , Weizhong AU - Mickens , Ronald E. JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 391 EP - 406 PY - 2023 DA - 2023/03 SN - 20 DO - http://doi.org/10.4208/ijnam2023-1016 UR - https://global-sci.org/intro/article_detail/ijnam/21539.html KW - Phase-lagging equation, fractional-order heat equation, numerical scheme, parameter estimation. AB -

Phase-lagging equation (PLE) is an equation describing micro/nano scale heat conduction, where the lagging response must be included, particularly under low temperature or high heat-flux conditions. However, finding the analytical or numerical solutions of the PLE is tedious in general. This article aims at seeking a fractional-order heat equation that is a good alternative for the PLE. To this end, we consider the PLE with simple initial and boundary conditions and obtain a fractional-order heat equation and an associated numerical method for approximating the solution of the PLE. In order to better approximate the PLE, the Levenberg-Marquardt iterative method is employed to estimate the optimal parameters in the fractional-order heat equation. This fractional-order alternative is then tested and compared with the PLE. Results show that the fractional method is promising.

Cui-Cui Ji, Weizhong Dai & Ronald E. Mickens. (2023). A Fractional-Order Alternative for Phase-Lagging Equation. International Journal of Numerical Analysis and Modeling. 20 (3). 391-406. doi:10.4208/ijnam2023-1016
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