Summary: In this note we treat the equations of fractional elasticity. After establishing well-posedness, we show a compactness result related to the theory of homogenization. For this, a previous result [the author, Asymptotic Anal. 82, No. 3–4, 271–294 (2013; Zbl 1280.35152)] in (abstract) homogenization theory of evolutionary equations has to be improved. The approach also permits the consideration of nonlocal operators (in time and space).