He heard Ibn Abbas reciting "And upon those who can endure it, a ransom of feeding a poor person" [Baqarah 2:184].Ibn Abbas said, "It is not abrogated. It refers to the elderly man and the elderly woman who are unable to fast, so they should feed a poor person in place of each day."
أنه سمع ابن عباس يقرأ: {وعلى الذين يطيقونه فدية طعام مسكين} قال ابن عباس: ليست منسوخة، هو الشيخ الكبير، والمرأة الكبيرة لا يستطيعان أن يصوما فليطعمان مكان كل يوم مسكينا.
Bukhari narrated it in the Tafsir (4505) from Ishaq, who said, Rawh informed us, Zakariya bin Ishaq narrated to us, Amr bin Dinar narrated to us from Ataa, who said, and then he related it.The abrogation that is established applies to the healthy person who is settled and required to fast, based on the words of Allah Most High, "So whoever among you witnesses the month, let him fast it" [Baqarah 2:185]. As for the frail elderly person who is unable to fast, he may break his fast, and he owes no make-up fast.As for the phrase, "let them feed a poor person in place of each day," this is the view of Ibn Abbas, and most scholars hold it. Anas, after he had grown old, used to feed a poor person bread and meat each day, and he would break his fast.The other view, which is one of the two positions of Shafii, is that feeding is not required of him, just as it is not required of the child who has not reached puberty, because Allah does not burden a soul beyond its capacity.See further detail in the Book of Fasting.