2/238. Be guardians of your prayers, and of the middle prayer* and stand up with devotion to Allah. 

4/103. .................... Worship at fixed hours hath been enjoined on the believers.

11/114 And establish regular prayers at the two (both) ends of the day and at the approaches of the night;** For those things, that are good remove those that are evil: Be that the word of remembrance to those who remember (their Lord): 

13/15 Whatever beings there are in the heavens and the earth do prostrate  themselves to God (Acknowledging subjection), with good-will or in spite of  themselves: so do their shadows in the morning and evenings.   

17/78 Establish worship at the sun's decline until the dark of night*** , and the (recitation of) the Quran at Fajr (dawn) . Lo! the recitation (Quran) at dawn is ever witnessed.

20/130 Bear then patiently what they say, and glorify your Lord by the praising (Hamd) of Him before sunrise**** and before its setting*****, and during parts of the hours of the night do also glorify (Him)****** and during parts of the day*******, that you may be well pleased

24/58 O ye who believe! let those whom your right hands possess, and those (children) among you who have not come of age ask your permission (before they come to your presence), on three occasions: before Fajr prayer (dawn); then while ye doff your clothes for the noonday heat; and after the Isha prayer (early night): these are your three times of undress: outside those times it is not wrong for you or for them to move about attending to each other: Thus does God make clear the Signs to you: for God is full of  knowledge and wisdom. 
[ Fajr,& Isha prayers mentioned by name]

30/17.  So glory be to Allah when ye enter the night and when ye enter the morning 

30/18. Unto Him be praise in the heavens and the earth! - and at the sun's decline  (evening) and in the noonday.

33/42 And glorify (Subhan Allah) Him morning and evening 

52/49 And................also praise Him,- and at the retreat of the stars!********
(Fajr time begins).

Notes:

* The Middle Prayer: Either Fajr (Dawn) prayer or Asr (Afternoon) prayers, whichever a person finds more difficult to offer on time.

**approaches of the night: soon after sunset (Maghreb & possibly Isha)

***the sun's decline until the dark of night: DZuhar, Asr, Maghreb & Isha prayers, from start of afternoon till first half of night.

****before sunrise: Fajr prayer (time ends at sunrise).

*****before sunset: time end before sunset; Asr  prayer & possibly also Dzuhar.

******parts of the hours of the night do also glorify: Maghreb &  Isha, from sunset till late night.

******* and during parts of the day: second half of day from early afternoon to just before sunset (Dzuhar & Asr time)

********at the retreat of the stars!: Fajr (dawn) prayer begening time.


                                                    Tahajjud (Optional prayers) 

17/79 And during a part of the night, pray Tahajjud beyond what is obligatory on you; maybe your Lord will raise you to a position of great glory (Maqam Mahmud).

25/64 Those who spend the night in adoration of their Lord prostrate and standing;  

50/40 And during part of the night, (also,) celebrate His praises, and (so likewise) after the postures of adoration.   

73/20 Thy Lord doth know that thou standest forth (to prayer) nigh two-thirds
of the night, or half the night, or a third of the night, and so doth a party of those with thee. But God doth appoint night and day in due measure He knoweth that ye are unable to keep count thereof. So He hath turned to you (in mercy): read ye, therefore, of the Qur'an as much as may be easy for you. He knoweth that there
may be (some) among you in ill-health; others travelling through the land, seeking of God's bounty ; yet others fighting in God's Cause, read ye, therefore, as much of the Qur'an as may be easy (for you); and establish regular Prayer and give regular Charity; and loan to God a Beautiful Loan. And whatever good ye send forth for your souls ye shall find it in God's Presence,- yea, better and greater, in Reward and seek ye the Grace of God: for God is Oft-Forgiving, Most Merciful. 

76/26 And part of the night, prostrate thyself to Him; and glorify Him a long night through.

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