On the Weak Solvability of a Fractional Viscoelasticity Model

The existence of a weak solution of a boundary value problem for a fractional viscoelasticity model that is a fractional analogue of the anti-Zener model with memory along trajectories of motion is proved. The rheological equation of the given model involves fractional-order derivatives. The proof relies on an approximation of the original problem by a sequence of regularized ones and on the theory of regular Lagrangian flows.