A Numerical-Analytical Method for Time-Fractional Dual-Phase-Lag Models of Heat Transfer (Advances in Applied Mathematics and Mechanics, 2022)
The aim of this paper is to present the backward substitution method forsolving a class of fractional dual-phase-lag models of heat transfer. The proposedmethod is based on the Fourier series expansion along the spatial coordinate over theorthonormal basis formed by the eigenfunctions of the corresponding Sturm-Liouvilleproblem. This Fourier expansion of the solution transforms the original fractional partial differential equation into a sequence of multi-term fractional ordinary differentialequations. These fractional equations are solved by the use of the backward substitution method. The numerical examples with temperature-jump boundary conditionand parameters of the tissue confirm the high accuracy and efficiency of the proposednumerical scheme.