A non-differentiable mechanical model (an alternative to Nottale's Scale Relativity Theory) considering that the particles movements takes place on Peano fractal curves is built. A Navier-Stokes type equation with an imaginary viscosity coefficient for a complex speed field, a Schrodinger-type equation and a hydrodynamic version of the non-differentiable mechanical model are obtained. The one body problem and the red-shift quantization in binary galaxies are investigated as an application.