Story here.
Obviously Ben Carson has not been a conviction politician.
Donald Trump registered as a Republican in New York in 1987 (under Reagan), 2009 (under Obama) and 2012 (under Obama). In 1999 (under Clinton) he had switched to the Independence Party, in 2001 (under Bush) to the Democrat Party, and in 2011 (under Obama) he affiliated with no one, according to this source.
So that's seventeen years (12 + 2 + 3) as a Republican, two as an Independence Party member, eight as a Democrat, and one year unaffiliated.
Obviously Donald Trump is a conflicted Republican, but can't possibly be described as an Obama Democrat, if anything just an anti-Bush Democrat.