  In the space and the time with a fractional dimensions the Lorents
transformations fulfill only as a good approach and become exact only when
dimensions are integer. So the principle of relativity (it is exact when
dimensions are integer) may be treated also as a good approximation and may
remain valid (but modified) in case of small fractional corrections to integer
dimensions of time and space. In this paper presented the gravitation field
theory in the fractal time and space (based on the fractal theory of time and
space developed by author early). In the theory are taken into account the
alteration of Lorents transformations for case including $v=c$ and are
described the real gravitational fields with spin equal 2 in the fractal time
defined on the Riemann or Minkowski measure carrier. In the theory introduced
the new "quasi-spin", given four equations for gravitational fields (with
different "quasi spins" and real and imaginary energies). For integer
dimensions the theory coincide with Einstein GR or Logunov- Mestvirichvili
gravitation theory.
