Why Do Ismailis Pray Three Times A Day Instead of Five?
The Qur’ān only mentions three specific prayer times:
And establish prayer at the two ends of the day and at the approach of the night. Indeed, good deeds do away with misdeeds. That is a reminder for those who remember. (11:114)
See also the below article about the history of prayer times in the Qur’ān: http://www.ismaili.net/Source/mumtaz/salat.pdf
Academic and historical study of Muslim tradition has shown that the idea of 5 prayer times emerged at least 100 years after the death of Prophet Muhammad and does not go back to Muhammad's historical teachings. Even in the Sunni tradition, the earliest sources used to prove the 5 prayers are contradictory and consist of two different Hadiths. One Hadith claims that the Prophet during his Mi'raj was ordered by God to have his community pray 50 times per day and then Moses told the Prophet to go back and negotiate with God to reduce the number; it is said that the Prophet negotiated until it was down to 5 times and he was embarrassed to reduce it anymore. Notwithstanding the theological problems of this Hadith, historical scholars have dated this Hadith to the end of the 1st century of Islam, i.e. mid-700s, 100 years after the Prophet., at the earliest (Juynboll dates it even later). Also, this Hadith was originally narrated by Anas b. Malik, not from the Prophet himself, and later sources forged a transmission line to take it back to the Prophet. Another Hadith contradicts this first Hadith and says only that Gabriel taught the Prophet the 5 prayers after he returned from his Mi'raj. Scholars have found that this second Hadith dates to 150 years after the Prophet, i.e. middle 2nd century of Islam (source: Stijn Aerts, "Ascension, Descension, and Prayer-Times in the Sīra and the Ḥadīth: Notes on Dating and Chronology," Der Islam 2017; 94(2): 385–422).
Even after all of this, Sunni Muslims disagree on how the 5 prayer times can be established --- sometimes ignoring the Hadiths and claiming they are in the Qur'an and other times, admitting the Qur'an contains no 5 prayers and using the above Hadiths. Unlike all of this contradiction, the Ismā‘īlī Muslims follow the guidance of Mawlana Hazar Imam who, as the legitimate bearer of the Prophet's authority and interpreter of the Qur’ān, has specified the number of prayers for his community to perform in the current times and contexts.