Praise be to Allah.
It is obligatory to prostrate during prayer on the seven parts that should touch the ground in prostration, which are: the forehead (with which the nose is included), the two hands, the two knees and the ends (toes) of the two feet, because of the report narrated by al-Bukhaari (812) and Muslim (490) from Ibn ‘Abbaas (may Allah be pleased with him), that the Messenger of Allah (blessings and peace of Allah be upon him) said: ““I have been commanded to prostrate on seven bones: the forehead – and he pointed to his nose – the hands, the knees and the ends of the feet (i.e., toes).”
Al-Nawawi (may Allah have mercy on him) said:
If he omits one of these parts then his prayer is not valid. End quote.
It says in Sharh Muntaha al-Iraadaat (1/432):
Prostrating on these seven bones, along with the nose, on the place where one is praying, whether it is the ground or a mat or anything else, is a pillar or essential part of the prayer if one is able to do that, because of the hadeeth of Ibn ‘Abbaas. End quote.
The perfect way is for the part which is meant to touch the ground in prostration should touch it fully, because when the Prophet (blessings and peace of Allah be upon him) prostrated, he made the tips of his toes point towards the qiblah (narrated by al-Bukhaari, 785); and because of the report narrated by Abu Dawood from Rifaa‘ah ibn Raafi‘ (may Allah be pleased with him) from the Prophet (blessings and peace of Allah be upon him) who said to the one who did not pray properly: “When you prostrate, make your prostration firm.” Classed as hasan by al-Albaani in Saheeh Abi Dawood. Making the part which is meant to touch the ground in prostration touch it fully is part of making the prostration firm.
It is acceptable to make the part which is meant to touch the ground in prostration touch it partially, according to the correct view of the Shaafa‘i and Hanbali madhhabs.
Al-Nawawi said in al-Majmoo‘ (3/423):
Prostrating on the forehead is obligatory, and there is no difference of opinion among us concerning that. It is better to prostrate on the whole forehead, but if one prostrates on it partially, that is acceptable, although it is disliked. This is the correct view which was stated by al-Shaafa‘i in al-Umm, and that was stated definitively by the majority of our companions. Ibn Kajj and al-Daarimi narrated another view that it is obligatory to place the whole forehead on the ground, but this is an odd and weak view. End quote.
Al-Mardaawi said in al-Insaaf (2/418):
It is acceptable to make the part which is meant to touch the ground in prostration touch it partially according to the correct view of our madhhab. Ibn Tameem said: It is permissible to prostrate on part of the hand and even on the back of the hand or the ends of the fingers; by the same token (it is permissible to prostrate) on some of the toes and some of the forehead… End quote.
It says in Mataalib Ooli al-Nuha (3/25):
It is acceptable to make the part which is meant to touch the ground in prostration touch it partially because the hadeeth does not state that the part should touch the ground fully. End quote.
Based on that, if a person prostrates on his feet and some of his toes touch the ground, his prayer is valid, but the Sunnah is to prostrate firmly on the parts of the body on which one rests during prostration as much as possible.
And Allah knows best.