In this talk, we first introduce a hyperbolic type evolution integral equation, that appears in the theory of fractional viscoelasticity. Then we prove existence and uniqueness of the solution in two frameworks. First we use the theory of semigroups, and then the Galerkin approximation method. Numerical approximation of the wave equation is formulated by the finite element method, and we prove the error estimates. Finally we extend the numerical approximation to solve the hyperbolic type integral equations and optimal order error estimates are proved.
