  Dissipative wave equations with critical quintic nonlinearity and damping
term involving the fractional Laplacian are considered. The additional
regularity of energy solutions is established by constructing the new
Lyapunov-type functional and based on this, the global well-posedness and
dissipativity of the energy solutions as well as the existence of a smooth
global and exponential attractors of finite Hausdorff and fractal dimension is
verified.
