Abstract
In this paper, a generalized thermoelastic model is established by incorporating two-fractional thermal conduction and multi-phase-lags. The Fourier heat conduction model is replaced by a more general formulation. Several models of generalized thermoelasticity including fractional derivatives are extracted from the considered model. The adopted model is examined to solve the problem of a semi-infinite medium subjected to a body force together with decaying heat source. Moreover, by utilizing the Laplace transform approach, the analytical solution of the problem is achieved. To illustrate the effects of decaying parameter, two fractional variables and also the external force, several numerical examples are conducted and the results are presented through some graphs and tables. Finally, our findings are justified compared to those reported in the literature.