  A four-dimensional timelike brane is considered as the boundary of the
$SAdS_{5}$ bulk background. Exploiting the CFT/FRW-cosmology relation, we
derive the self-gravitational corrections to the first Friedmann-like equation
which is the equation of the brane motion. The additional term that arises due
to the semiclassical analysis, can be viewed as stiff matter where the
self-gravitational corrections act as the source for it. This result is
contrary to standard analysis that regards the charge of $SAdS_{5}$ bulk black
hole as the source for stiff matter. A very interesting feature of the
solutions of FRW equation is that they all (for $k=0,\pm1$) have a
non-vanishing minimum value for the scale factor.
