  In recent years the problem of correct description of quantum fluids in the
confined geometry at nanoscale length has emerged. It has been recognized that
the quantum fluids at these circumstances can be considered as a new state of
quantum matter due to close values between characteristic lengths for these
quantum liquids and the size of geometrical confinement and significant
contribution from the surface atoms. So one has to apply new physics to
describe such systems with taking into account their complex nature. For
example, last two years the attempts to develop the fractionalized two-fluid
hydrodynamics for nanoporous media with fractal dimensions have been made. The
actuality of such new hydrodynamics becomes very clear for the last development
in chemical synthesis of different kind of aerogels with nanopore structure as
well as numerous studies of nanoporous substances. One of the interesting
obtained results that density waves (the first sound) and temperature waves
(the second sound) become strong coupled even in the absence of viscosity, so
it is purely geometric effect of fractal space of nanopores. In the present
report we will review the procedure, results and discuss the issues for this
approach.
