This paper is concerned with the investigation of the temperature, displacement, and stresses due to thermal shock loading on the inner surface cavity in an infinite medium with a cylindrical cavity. The governing equations will be taken into the context of the fractional order generalized thermoelasticity theory. In the Laplace transform domain, the form of a vector-matrix differential equation has been written for the basic equations, which is then solved by an eigenvalue approach. The result provides a motivation to investigate the effect of fractional parameter on the physical quantities.