That is instead of putting right hand over left like the other Madhhab keep the hands by their sides.
Is praying the hands to the sides really the view of Malik?
First of all note that the opinion that imam Malik disliked putting the right hand over the left hand is based on the unique statement of his student Abdurrahman ibn al-Qassim in al-Mudawana. Earlier scholars of this school (especially hadith specialists) like al-Qadi 'iyad even said that this is a misinterpretation of the statement of ibn al-Qassim, as what was frowned upon is putting one hand on the other in nafl prayer while leaning against a wall or something to keep in position. While ibn 'Abd-al-Barr that almost all narrations quoting a position for the hand quote the right hand over left option (ibn 'abd-al-Barr had shafi'i tendencies).
Other students of Malik like those from Medina didn't confirm this or maybe even held the opinion that putting right hand on left hand is sunnah (those from 'Iraq)!
One must add that ibn al-Qassim didn't see his teacher during at least the last 7 years of Malik's lifetime, so he might not know what was his last opinion on that matter.
But on the other hand many other scholars have statements quoting that leaving the hands aside is their preference among them imam a-Shafi'i, there's even a statement of al-Laith ibn Sa'ad rejecting that putting the right hand on the left hand is sunnah!
It is also known that the sahabi Abdullah ibn az-Zubair never performed putting the right hand on the left and used to take away or decollate the hands of a praying people if he saw them doing so (according to al-Khateeb al-Baghdadi in his tarikh)!
The view of the Maliki madhhab or the established madhhab is based on mukhtassar Khalil in which the author pretends that sadl is the preferred way and qabd is disliked. But it doesn't represent the view of all scholars of this school as said before!
Also note that all ahadith in al-Muwatta' of imam Malik which might be used as an evidence for putting one hand on the other have weaknesses and most if not all ahadith on this matter are only quoted in the sunan books, which means they are not that strong!
Defining some terms
Note that some call leaving the hands by the sides (of the leg) al-Irsaal الإرسال or al-Isbaal الإسبال while the malikis often use the term as-Sadl السدل, while they refer to putting the right hand on the left by al-Qabd القبض.
Some sources for keeping the hands by the sides
For example on the authority of Mo'ad ibn Jabal () in at-Tabarni's al-Kabir:
" كان النبي صلى الله عليه وسلم إذا كان في صلاته رفع يديه قبالة أذنيه ، فإذا كبر أرسلهما ثم سكت ، وربما رأيته يضع يمينه على يساره ، فإذا فرغ من فاتحة الكتاب سكت ، فإذا ختم السورة سكت ، ثم يرفع يديه قبالة أذنيه ، ويكبر ويركع ، وكنا لا نركع حتى نراه راكعا ، ثم يستوي قائما من ركوعه ، حتى يأخذ كل عضو مكانه ، ثم يرفع يديه قبالة أذنيه ، ويكبر ويخر ساجدا ، وكان يمكن جبهته وأنفه من الأرض ، ثم يقوم كأنه السهم لا يعتمد على يديه ، وكان إذا جلس في آخر صلاته اعتمد على فخذه اليسرى ، ويده اليمنى على فخذه اليمنى ، ويشير بإصبعه إذا دعا ، وكان إذا سلم أسرع القيام " .
I'll translate only the necessary part:
When praying the Prophet (peace and blessings be upon him) used to raise his hands towards his ears, if he made the takbir he let them down (by his sides). then he kept quite (for a moment), and maybe I've seen him putting the right hand on the left hand ...
This hadith shows that both options seem to have been witnessed, but the fact that the option of putting one hand on an other is secondly quoted might indicate that it was not the most common one!
There's also the hadith of abu Humaid al-Sa'idi (in sunan abi Dawod):
I am one among you who is more informed of the way the Messenger of Allah (ﷺ) prayed. They said: Why, By Allah, you did not follow him more than us, nor did you remain in his company longer than us? He said: Yes. They said: Then describe (how the Prophet prayed). He said: When the Messenger of Allah (ﷺ) stood up to pray, he raised his hands so as to bring them opposite his shoulders, and uttered the takbir (Allah is the most great), until every bone rested in its place properly: then re recited (some verses from the Quran); then he uttered the takbir (Allah is most great), raising his hands so as to bring them opposite his shoulders; then he bowed; placing the palms of his hands on his knees and keeping himself straight, neither raising nor lowering his head; then raised his head saying: “Allah listens to him who praise Him”; then raised his hands so as to bring them exactly opposite to his shoulders; then uttered: “Allah is most great”; then lowered himself to the ground (in prostration), keeping his arms away from his sides; then raised his head, bent his left foot and sat on it, and opened the toes when he prostrated: then he uttered: “Allah is most great”; then raised his head, bent his left foot and sat on it so that every bone returned to its place properly; then he did the same in the second (rak’ah). At the end of the two Rak’ahs he stood up and uttered the takbir (Allah is most great), raising his hands so as to bring them opposite to his shoulders; then he bowed, placing the palms of his hands on his knees and keeping himself straight, neither raising or lowering his head: then raised his head saying: “Allah listens to him who praises Him”; then raised his hands so as to bring them exactly opposite his shoulders; then uttered: “Allah is most great”; then lowered himself to the ground (in prostration), keeping his arms away from his sides; then raised his head, bent his left foot and sat on it, and opened the toes when he prostrated himself; then he prostrated; then uttered: “Allah is most great”; then raised his head, bent his left foot and sat on it so that every bone returned to its place properly; then he did the same in the second (rak’ah). At the end of two rak’ahs he stood up and uttered the takbir (Allah is most great), raising his hands so as to bring them opposite to his shoulders in the way he had uttered the Takbir (Allah is most great) at the beginning of the prayer; then he did that in the remainder of his prayer; and after prostration which if followed by the taslim (salutation) he out his left foot and sat on his left hip. They said: You have spoken the truth. This is how he(peace be upon him) used to pray.
See also in sunan ibn Majah.
Here the point is that logic says that the bones of the arms rest properly when they are at the sides, note that among those sahaba whom witnessed this was abu Qatadah one of the narrators of the putting right hand over left hand! Ibn Hajjar al-'Asqalani could quote the names of 6 out of these 10 sahaba, among them was abu Hurairah,sahl ibn Sa'ad and Muhammad ibn Maslamah! Also note that abu Dawod heard the hadith from Ahmad ibn Hanbal himself!
There's also a version of this hadith compiled by ibn Hebban.
Ibn 'Abd al-Barr said that Malik has got the hadith regarding this view from Abdullah ibn al-Hassan!
Some criticism on the hadiths of the opposite view
Let' start with the two ahadith from al-Muwatta'
"People used to be ordered to place their right hands on their left forearms in the prayer."
Abu Hazim added, "I know for sure that Sahl traces that back to the Prophet, may Allah bless him and grant him peace." (al-Muwatta' and sahih al-Bukhari)
Al-Bukhari already criticized the Hadith himself by quoting a corrected verison of the statement of abu Hazim in the passive voice which makes this hadith mursal (disconnected):
قَالَ إِسْمَاعِيلُ يُنْمَى ذَلِكَ. وَلَمْ يَقُلْ يَنْمِي.
And this is the only hadith on qabd compiled by al-Bukhari, but it doesn't reach the condition of musnad hadith which would qualify it as-Sahih according the title of the book! Mulla 'ali al-Qari even assumed that "the order in this hadith" refers to the time of the caliphs not to the time of the Prophet()!
And the other hadith:
'As long as you do not feel ashamed, do whatever you wish', the placing of one hand on the other in prayer (one places the right hand on the left), being quick to break the fast, and delaying the meal before dawn." (al-Muwatta')
Here Malik for once narrated a hadith from a man from 'Iraq and had chosen a bad narrator as Abd al-Karim ibn Abi'l-Mukhariq al-Basri عَبْدِ الْكَرِيمِ بْنِ أَبِي الْمُخَارِقِ الْبَصْرِيِّ was considered as matruk (left out as he was not trustworthy as a narrator). Some said that Malik was blinded by al-Mukhariqs attitude, but this man was not from his location so he didn't know him well enough. An-Nasa'i said "Malik didn't narrate from any weak narrator with the exception of 'Abd al-Karim"! Ibn 'abd al-Barr quoted a statement of Malik: "I was blinded by the frequence of 'Abd-al-Karim's weeping in the mosque"
While imam Muslim also only compiled one single narration with weaknesses in his sahih on this matter:
He saw the Messenger of Allah (ﷺ) raising his hands at the time of beginning the prayer and reciting takbir, and according to Hammam (the narrator), the hands were lifted opposite to ears. He (the Holy Prophet) then wrapped his hands in his cloth and placed his right hand over his left hand. And when he was about to bow down, he brought out his hands from the cloth, and then lifted them, and then recited takbir and bowed down, and when (he came back to the erect position) he recited:" Allah listened to him who praised Him." And when he prostrated, he prostrated between his two palms. (sahih Muslim)
This hadith has three weaknesses:
1. The narrator 'Alqamah ibn Wa'il عَلْقَمَةَ بْنِ وَائِلٍ who is narrating from his father while ibn Hajar said he didn't as he didn't reach the age to be able to narrate before his fathers death! (tahdeedb at-Tahdeeb volume 2 page 5).
2. The different versions from sunan abi Dawod 1, 2, 3 create a confusion.
3. From the matn (the content) as it is contradictory if we check all the narrations of the same narrator.
An other point is that 'Asim ibn Kulaib (a narrator of the versions of abu Dawod) was also considered as weak or unreliable!
Some scholars tried to show that putting one hand on the other is following the way of people of the book at the beginning of Islam, but was no more in use later based on statement such as:
كَأَنِّي أَنْظُرُ إِلَى أَحْبَارِ بَنِي إِسْرَائِيلَ وَاضِعِي أَيْمَانِهِمْ عَلَى شَمَائِلِهِمْ فِي الصَّلَاةِ " (Source: مصنف ابن أبي شيبة musanaf ibn abi Shaybah)
which might be translated:
As if I was looking at (watching) the Rabi's of bani Israel putting their right hands on their left hands in the prayer
This is also one interpretation of the second hadith from al-Muwatta'!
Ibn abi Shaybah in his book has two chapters one quoting ahadith and narrations of qabd and others of irsaal! In which you may find that such people as Abullah ibn az-Zubair, ibn al-Mussyaib, ibn Sireen, al-Hassan al-Basri, Sa'id ibn Jubayr whom followd the later. Many of the qabd narrations seem to confirm that some scholars disliked forms of qabd because that looked like the way people of the book used to do, among them Mujahid (see here in Arabic)
Also irsaal was widely confirmed by the Imam's of shi'a even if ibn Shaybah here presents an opposite narration on the authority of 'Ali ibn abi Talib as an interpretation of verse 2 from surat al-Kawthar (see here in Arabic).