Using fractional derivatives in the sense of new Caputo, we study a problem in the fractional-order theory of thermoelasticity. The problem concerns an elastic half-space. Asymptotic expansions are used. The approximate solution obtained is valid for small times, but the conducted study of wave propagation is exact for all times. We found that there are two waves emanating in the system. One wave, which is mainly mechanical, is traveling with a finite speed. The other wave, which is mainly thermal, was found to have infinite speed. The Laplace transform technique is used. Graphical results are presented and discussed for the relevant functions.
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