Expiation for not praying

Whoever omits one or more obligatory prayers with no excuse has to repent to Allaah sincerely, and he does not have to make them up or offer any expiation (kafaarah), because omitting the obligatory prayers deliberately is major kufr, as the Prophet (peace and blessings of Allaah be upon him) said: “The covenant that stands between us and them is prayer; whoever gives it up is a kaafir.” Narrated by Ahmad, 22428; al-Tirmidhi, 2621; al-Nasaa’i, 462. And he said: “Between a man and shirk and kufr there stands his giving up prayer.” Narrated by Muslim, 242. There is no expiation for that except sincere repentance. See Fataawa al-Lajnah al-Daa’imah, 6/50 

Prayer is an act of worship that is to performed at specific times, and whoever does not do an act of worship that is tied to a specific time – such as prayer and fasting – until that time is over, with no excuse, then repents, does not have to make up what he omitted, because this act of worship has been limited by the Lawgiver to the beginning and ending of that time. 

Fataawa al-Shaykh Ibn ‘Uthaymeen, 1/322. 

But if a person misses a prayer for a valid excuse such as sleeping or forgetting, his expiation is to offer the prayer when he remembers it, and there is no other expiation required, as the Prophet (peace and blessings of Allaah be upon him) said: “Whoever forgets a prayer or sleeps and misses it, let him pray it when he remembers, and there is no other expiation for it but that.” 

Al-Bukhaari, 572; Muslim, 1564 

And Allaah knows best.