Global attractors of the degenerate fractional Kirchhoff wave equation with structural damping or strong damping

Abstract This article deals with the degenerate fractional Kirchhoff wave equation structural damping or strong damping. The well-posedness and existence of global attractor in natural energy space by virtue Faedo-Galerkin method estimates are proved. It is worth mentioning that results this cover case possible degeneration (or even negativity) stiffness coefficient. Moreover, under further suitable assumptions, fractal dimension shown to be infinite using Z 2 {{\mathbb{Z}}}_{2} index theory.