Can I pray the missed obligatory prayers after the dawn prayer, or the Asr prayer, if I am fear I will miss the present obligatory prayers?

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.

Allaah ordained us to perform the five daily prayers at their prescribed fixed times. Allaah Says (what means): {… Verily, the prayer is enjoined on the believers at fixed hours.} [Quran 4: 103]

Moreover, the Prophet explained the times of prayers by his words and deeds as well. The Prophet said: "Perform the prayer as you see me praying" [Al-Bukhari]

Therefore, if one had missed to perform the prayer at its prescribed fixed time, he should perform it right after remembering it. The Prophet said: "If one of you forgets a prayer or sleeps through its time, (as in a narration), he should pray it as soon as he remembers it, and there is no expiation for it save that." [Al-Bukhari and Muslim]

Allah Says (what means): {… and establish prayer for My remembrance..} [Quran 20:14]

The majority of the Muslim scholars are of the opinion that the missed prayers should be made up at any time: day, night, during the time when performing the prayer is forbidden, and at the time of sunrise or sunset.

However, the Hanafi School of jurisprudence is of the view that the prohibition of performing the prayer at certain times is well established and even the missed obligatory prayers should not be offered at that time.

In any case, the questioner should hasten to perform the missed prayers at any time of day or night (i.e. after Fajr or Asr).

If he is afraid the time of the current prayer will end and the missed prayers are five or more, then he should offer the current prayer. If the missed prayers are only four or less,  then, in this case, he should make them up even if the time of the current prayer ends. This is the opinion of the Maaliki School of jurisprudence and those who agree with them.

Nonetheless, some Muslim scholars hold the opinion that if one fears the time of the current prayer to end, he should perform that prayer first.

However, both practices are acceptable since there is no specific evidence in this matter. Know that the difference of opinions of the scholars in such matters is a mercy and their agreement is evidence.

Allaah Knows best.