Is the prayer of one who woke up late, a few minutes before Asr, and the call to Asr was made while the worshiper was engaged in praying Dhuhr alone; considered "adaa'" (performed on time) or "qadaa'" (performed as a make-up), and did he catch it? And what is the meaning of the word "adaa'" in the fatwas related to the sayings of the Malikis and the majority of scholars regarding one who did not intend to make up a prayer whose time had elapsed, and that Dhuhr and Asr share a common time? And if the mother caught the prayer behind her son and then saluted with him, is she to stand up and perform the missed rak'ahs after the salutation, or is she to repeat the prayer from the beginning?

The question includes several points:

1. The time for Dhuhr ends with the entry of Asr time according to the majority of scholars. So, if the adhan for Asr is called after its time has begun, your individual Dhuhr prayer is considered a qada (make-up) prayer by the majority, and an ada’ (on-time) prayer by the Malikis, who hold that the necessary time for Dhuhr extends until sunset.

2. Ada’ is performing all or part of the prayer before its time expires, while qada is performing it after its time has expired.

3. If your mother prays behind you and catches the entire prayer, she salutes with you. If she misses one or more rak'ahs, she makes up what she missed after you salute, and her prayer is valid whether your prayer was ada’ or qada.

4. One must take measures to wake up for prayer.