<p>This paper investigates a dynamic frictional contact problem for a viscoelastic body interacting with a foundation. The constitutive law, equation of motion, and boundary conditions all involve time-fractional derivatives. The normal compliance condition and friction law are modeled via Clarke subdifferentials, leading to a time-fractional hemivariational inequality. We reformulate it as an equivalent problem incorporating both fractional derivatives and integrals. By applying the Banach fixed-point theorem alongside existing results for hemivariational inequalities, we establish the existence of a unique weak solution. Furthermore, a priori error estimates are derived for semi-discrete and fully-discrete numerical schemes. Numerical simulations are presented to verify the theoretical conclusions.</p>