Every fluid problem is greatly affected by its boundary conditions, especially the near-shore seabed could produce an irrevocable harm when a tsunami wave is approaching, and a real-life mathematical model could stave off the worst effect. This paper assumes that the unsmooth seabed is a fractal surface, and fractal-fractional governing equations are established according to physical laws in the fractal space. The geometrical potential theory is used to explain the force produced by the wave surface, and Kong-He friction law is applied to further figuring out the local and memory properties of the friction along the fractal boundary. This paper aims at studying tsunami waves in a fractal space, rendering a reliable mathematical model for both prediction of the tsunami motion and the coastal protection.

每个流体问题都受到其边界条件的极大影响，尤其是当海啸逼近时，近岸海底可能会产生不可挽回的伤害，而现实生活中的数学模型可以避免最坏的影响。本文假设不光滑海底是分形表面，根据分形空间中的物理定律建立了分形-分数阶控制方程。利用几何势理论来解释波面产生的力，并应用孔合摩擦定律进一步弄清楚分形边界上摩擦力的局部和记忆特性。本文旨在研究分形空间中的海啸波，为海啸运动预测和海岸保护提供可靠的数学模型。