Abstract
In this article, a theoretical framework for problems involving fractional equations of hyperbolic type arising in the theory of viscoelasticity is presented. Based on the Galerkin method, a variational problem of the fractionary viscoelasticity is studied. An appropriate functional setting is introduced in order to establish the existence, uniqueness and a priori estimates for weak solutions. This framework is developed in close concordance with important physical quantities of the theory of viscoelasticity.
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