Fidyah is an obligation for those who are of sound mind but are unable to fast due to old age, a chronic illness, or a continuous excuse, and for whom it is not expected that they will be able to fast in the future.
Alzheimer’s disease has varying degrees. If, despite certain difficulties, the person retains sound understanding and is aware of what he is doing, then he is required to fast; if he is unable to do so and it is not expected that he will be able to fast thereafter, then he is required to pay fidyah.
However, for those who have completely lost their mental faculties, fasting is not obligatory; likewise, neither making up the fasts (qaḍāʾ) nor paying fidyah is obligatory. This is because sound intellect is a condition for religious responsibility. When intellect is absent, responsibility does not apply. Nevertheless, if at some point the person’s mental capacity returns, he becomes responsible again for fasting, as well as for other acts of worship and religious rulings. No make-up (qaḍāʾ) or fidyah is required for the period during which mental capacity was absent.