Abstract
In this work, we constructed a mathematical model of an infinite elastic body with a spherical cavity in the context of the theory of generalized thermoelasticity with fractional order strain. The bounding plane of the cavity is connected with thermal shock. Laplace transform techniques are used, and the inversions are computed numerically using a method based on Fourier expansion techniques of Tzuo method. Some especial comparisons have been illustrated in figures to discuss the effects of the two-temperature and the fractional order parameters.