Whether or not this is possible for you will very much depend on your circumstance.
It is definitely possible in principle to buy out your ex partners share, but your personal circumstances will dictate your eligibility.
The best advice I can give is to contact a good independent
mortgage broker such as myself. A good mortgage broker should be able to give you an idea of whether or not you will be able to get a mortgage on your own, suugest a good mortgage lender and talk through any other issues you have.
Sorry I can't give you a definite answer but without looking at your whole situation that would be impossible.