Assuming non‐Fourier thermal effects, Tzou's dual‐phase‐lag model has been applied to introduce the governing heat conduction equation in the presented mathematical model. Moreover, in order to design a well‐posed dual‐phase‐lag model, the governing time fractional dual‐phase‐lag heat equation has been established by introducing conductive temperature and thermodynamical temperature, satisfying the two‐temperature theory. Due to the application of phase lags τ_Ω, τ_Θ satisfying τ_Ω > τ_Θ, the finite speed of thermal wave propagation has been achieved. The corresponding governing equations of motion and stresses have been considered in two‐dimensional bounded spherical domain. The spherical boundaries are assumed to be traction free. The Laplace and the Legendre integral transforms have been applied to obtain the analytical solutions of conductive and thermodynamical temperatures, displacement components, and thermal stresses. The Gaver–Stehfest algorithm has been employed to achieve the time domain inversions of Laplace transforms numerically, satisfying the Kuznetsov convergence criteria. Classical, fractional and generalized thermoelasticity theories has been recovered theoretically and numerically as well for various fractional orders and phase‐lags.

中文翻译：

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空心球的非傅立叶分数阶热弹性二维模型

假设非傅立叶热效应，Tzou的双相滞后模型已被用于在所介绍的数学模型中引入控制热传导方程。此外，为了设计一个良好的双相滞后模型，通过引入传导温度和热力学温度，并满足两温理论，建立了控制时间分数双相滞后热方程。由于相位滞后的应用τ _Ω，  τ _Θ满足τ _Ω  >  τ _Θ，已经达到了热波传播的有限速度。在二维有界球域中考虑了相应的运动和应力控制方程。假定球形边界没有牵引力。已应用拉普拉斯（Laplace）和勒让德（Legendre）积分变换来获得传导和热力学温度，位移分量和热应力的解析解。Gaver–Stehfest算法已被用来实现Laplace变换的时域反演，其数值满足Kuznetsov收敛准则。对于各种分数阶和相位滞后，经典，分数和广义的热弹性理论已经在理论和数值上得到了恢复。