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

中文翻译：

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具有结构阻尼或强阻尼的简并分数基尔霍夫波动方程的全局吸引子

摘要 本文研究了带有结构阻尼或强阻尼的简并分数阶基尔霍夫波动方程。利用Faedo-Galerkin方法和能量估计证明了自然能量空间中全局吸引子的适定性和存在性。值得一提的是，本文的研究结果涵盖了刚度系数可能退化（甚至为负）的情况。此外，在进一步合适的假设下，