Abstract <p>In this work, a half-space with variable thermal conductivity and diffusivity is investigated in the context of fractional thermoelastic diffusion theory. The half-space is subjected to thermal and chemical shocks. Laplace transforms, along with their numerical inversion, are employed to solve the problem. To validate the theoretical derivations, the model is degraded to the simpler case and the results are compared with those obtained by Sherief and Saleh. Then, the influence of fractional order parameters, acting time, small coefficients of thermal conductivity variation, and small coefficients of diffusion variation on dimensionless physical quantities are depicted graphically.</p>