About the Appeal
A person who cannot fast due to extreme weakness, old age or has a chronic illness (or other health reason ) from which they have no apparent hope of recovery is Islamically allowed to feed an indigent person, or give away its cost, instead of as atonement for every fast. This is called Fidiyah in shariah.
“(The prescribed fast is for) a certain number of days. Whoever among you does not fast on those days because you are sick or on a journey, then (you should fast) the same number of days on other days. Those who are able to fast are also required to pay a fee (which is equivalent to the cost) of feeding a desperate person. ” (Al-Baqarah 2:184)