  We consider brane cosmologies within the context of five-dimensional actions
with O(a') higher curvature corrections. The actions are compatible with bulk
string amplitude calculations from heterotic string theory. We find wrapped
solutions that satisfy the field equations in an approximate but acceptable
manner given their complexity, where the internal four-dimensional scale factor
is naturally inflating, having an exponential De-Sitter form. The temporal
dependence of the metric components is non-trivial so that this metric cannot
be factored as in a conformally flat case. The effective Planck mass is finite
and the brane solutions localize four-dimensional gravity, while the
four-dimensional gravitational constant varies with time. The Hubble constant
can be freely specified through the initial value of the scalar field, to
conform with recent data.
