Advanced thermoelastic heat conduction model with ?two fractional parameters and phase-lags

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 asemiinfinite 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.