A Numerical-Analytical Method for Time-Fractional Dual-Phase-Lag Models of Heat Transfer

Abstract

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.