Assuming non-Fourier thermal effects, Tzouâ€™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 stable 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 the heat conduction equation became hyperbolic. 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 values.