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 - <p style="text-align: justify;">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.</p>