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 is His slave and Messenger.
There is no reported recitation in the Sunnah that is to be said after yawning or burping; it has only been reported that one should say “alhamdulillaah” (praise be to Allaah) after sneezing and repel yawning as much as possible.
Al-Bukhari entitled a chapter called The Chapter of what is desirable (to say) when sneezing and what is disliked when yawning:
“Allaah loves the act of sneezing and dislikes the act of yawning. When any one of you sneezes and says ‘alhamdulillaah’ (praise be to Allaah), then he has the right that every Muslim who hears him says to him ‘yarhamuk Allaah’ (may Allaah have mercy upon you). Yawning, however, is from the Shaytaan (the devil), so if any of you feels the urge to yawn, he should resist it as much as he can, for if he makes a yawning sound, the Shaytaan laughs at him.”
The Prophet mentioned saying alhamdulillaah (praise be to Allaah) after sneezing, which Allaah likes, and he mentioned resisting yawning, which Allaah dislikes, as much as possible, and the Prophet did not mention any statement that is to be said after yawning.
Imaam Muslim reported a hadeeth with the following wording, “If one of you yawns, let him put his hand on his mouth, as the devil enters.”
If a Muslim sneezes and praises Allaah, then his Muslim brother should say to him, "‘Yarhamuka Allaah’ (may Allaah have mercy upon you). The person who sneezed replies by saying, ‘Yahdeena wa yahdeekum Allaah’ (May Allaah guide us and you).”
Abu Hurayrah narrated that the Prophet said, “When one of you sneezes, he should say, 'Alhamdulillaah' (All praise be to Allaah), and his brother or companion should say to him, 'Yarhamuk Allaah.' Then the person who sneezed says, 'Yahdeekum Allaah wa yuslihu baalakum' (May Allaah guide you and rectify your affairs).”
In case the person who sneezed did not say alhamdulilllaah, then one does not say, 'Yarhamuk Allaah' to him.
Anas narrated that two men sneezed while in the company of the Prophet and the Prophet said to one of them, “Yarhamuk Allaah” while he did not say this to the other man. He was asked why and he replied, “This man praised Allaah, and this man did not.” [Al-Bukhari, Muslim, Abu Dawood, An-Nasaa’i, Ibn Maajah, and Ahmad]
One may say “yarhamuk Allaah” to the person who sneezed three times, and if he sneezes more than this, then one may supplicate Allaah to cure him.
Ibn Maajah reported, “A person who sneezes (more than once), one may say to him yarhamuk Allaah up to three times. If he sneezes more than three times, then he has a cold.”
It is for this reason that an-Nawawi said, “If a person sneezed repeatedly, then the Sunnah is that he should say ‘yarhamuk Allaah’ each time until three times, and if the person sneezes more than three times and it seems that he has a cold, then he can supplicate Allaah for his recovery.”
However, if the person who sneezes is a non-Muslim, then one does not say to him, ‘yarhamuk Allaah’; rather, he says to him, “Yahdeekum Allaah wa yuslihu baalakum (May Allaah guide you and rectify your affairs).”
Abu Dawood entitled a Chapter: Chapter of what to say to a person who sneezes who is a Thimmi (a non-Muslim living in a Muslim state): “Abu Moosa al-Ash'ari said, 'The Jews used to sneeze in the presence of the Prophet hoping that he would say to them ‘Yarhamukum Allaah’, but he used to say to them ‘Yahdikumullaah wa yuslihu baalakum’.' [Ahmad and at-Tirmithi, and an-Nasaa’i narrated it under the Chapter: What to say to the people of the book when they sneeze.]”
Allaah knows best.