Abstract
A new mathematical model of poro-thermoelasticity has been constructed in the context of a new consideration of heat conduction with fractional order. One-dimensional application for a poroelastic half-space saturated with fluid is considered. The surface of the half-space is assumed to be traction-free, permeable, and subjected to heating. The Laplace transform technique is used to solve the problem. The inversion of the Laplace transform will be obtained numerically and the numerical values of the temperature, stresses, strains, and displacements will be illustrated graphically for the solid and the liquid.