<p>This study develops a fractional thermoelasticity theory to investigate the thermal shock response in anisotropic circular hollow cylinders, ensuring thermodynamic consistency. Using a fractional derivative model with one relaxation time, the research derives analytical solutions for temperature, deformation, and stress fields via integral transform techniques. Laplace transform and its numerical inverse are used. The cylinder is subjected to thermal shocks that may be either nearly equal or distinctly different at its inner and outer surfaces. Numerical results, illustrated through diagrams, highlight the role of fractional calculus in modeling thermal–mechanical interactions more accurately than classical non-fractional theories. The study is driven by the need for a more reliable framework to predict thermal shock behavior in anisotropic cylindrical structures, where classical models fall short. Its outcomes support improved design of pipelines and similar components by guiding material selection and offering insights for reducing thermally induced stresses.</p>