All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If the condition of the one who suffers from Alzheimer worsens and he becomes unable to fast while his mental faculties and realization are still intact, then he is allowed to break the fast and feed a poor person for each day that he misses as long as the disease is permanent and chronic. However, if the disease becomes very severe and the patient becomes unable to realize or grasp what is going on around him, then he neither has to fast nor offer an expiation in the first place.
Allaah Knows best.