For starters, Carbon has some pretty convenient methods for instantiation. You can do something like
Carbon::createFromFormat('Y-m-d H', '1975-05-21 22')
I would peruse the instantiation section of the Carbon documentation to find what fits your needs most closely.
http://carbon.nesbot.com/docs/#api-instantiation
P.S. You're getting no results because you're passing the same dates to the constructor. Vanilla dates like that will evaluate to Midnight, or 00:00:00. So you are searching between 29-09-2016 00:00:00 and 29-09-2016 00:00:00, an interval of 0 milliseconds. Makes sense to get no results! I'm not sure if you would even get results for something that happened at exactly 29-09-2016 00:00:00.
Good luck