Abstract
Recently, fractional calculus theory has been successfully employed in generalized thermoelasticity theory and several models with fractional order have been introduced. In this work, a fractional thermoelastic modified Fourier's Law with phase lag and two different fractional-orders has been constructed. The previous fractional models of thermoelasticity introduced by Sherief et al. [1], Ezzat [2] and Lord and Shulman [3] as well as classical coupled thermoelasticity [4] follow as limiting cases. This proposed model is applied to an infinitely annular cylinder that is subject to time-dependent surface temperatures, and whose surfaces are free of traction. The method of the Laplace transform is employed to get the solutions of the field variables. A numerical technique is utilized to invert the Laplace transforms. Some results are presented in tables and figures to extract the effects of fractional order parameters on all variables studied. The theory's predictions have been checked and compared to previous models.