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In this article a theoretical framework for problems involving fractionalequations of hyperbolic type arising in the theory of viscoelasticity ispresented. Based on the Galerkin method, a variational problem of thefractionary viscoelasticity is studied. An appropriate functional setting isintroduced in order to establish the existence, uniqueness and a prioriestimates for weak solutions. This framework is developed in close concordancewith important physical quantities of the theory of viscoelasticity

Variational formulation for fractional hyperbolic problems in the theory of viscoelasticity