  Fractals emerge everywhere in nature, exhibiting intricate geometric
complexities through the self-organizing patterns that span across multiple
scales. Here, we investigate beyond steady-states the interplay between this
geometry and the vanishing dynamics, through phase-transitional thermal melting
and hydrodynamic void collapse, within fractional continuous models. We present
general analytical expressions for estimating vanishing times with their
applicability contingent on the fractality of space. We apply our findings on
the fractal environments crucial for plant growth: natural soils. We focus on
the transport phenomenon of cavity shrinkage in incompressible fluid,
conducting a numerical study beyond the inviscid limit. We reveal how a minimal
collapsing time can emerge through a non-trivial coupling between the fluid
viscosity and the surface fractal dimension.
