TY - JOUR
T1 - A Numerical-Analytical Method for Time-Fractional Dual-Phase-Lag Models of Heat Transfer
AU - Lin , Ji
AU - Reutskiy , Sergiy
AU - Feng , Wenjie
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 666
EP - 702
PY - 2022
DA - 2022/02
SN - 14
DO - http://doi.org/10.4208/aamm.OA-2020-0237
UR - https://global-sci.org/intro/article_detail/aamm/20280.html
KW - Heat transfer, dual-phase-lag model, fractional partial differential equation, semi-analytical method.
AB - <p style="text-align: justify;">The aim of this paper is to present the backward substitution method for
solving a class of fractional dual-phase-lag models of heat transfer. The proposed
method is based on the Fourier series expansion along the spatial coordinate over the
orthonormal basis formed by the eigenfunctions of the corresponding Sturm-Liouville
problem. This Fourier expansion of the solution transforms the original fractional partial differential equation into a sequence of multi-term fractional ordinary differential
equations. These fractional equations are solved by the use of the backward substitution method. The numerical examples with temperature-jump boundary condition
and parameters of the tissue confirm the high accuracy and efficiency of the proposed
numerical scheme.</p>