There is great controversy in the world today over the question of the identity of the "the god" which the nation of Islam refers to as Allah.
Most people, especially Christians and Jews, do not believe that the God of the Muslim people in their inception is the same god that they worship today.
Granted, this religion of Islam on some, even many points, has strayed from it's roots, but that does not change the origin of the people nor does it change what the God of Abraham, Isaac, and Jacob has to say about them.
(Gen 16:11) And the angel of the LORD said unto her, Behold, thou art with child, and shalt bear a son, and shalt call his name Ishmael; because the LORD hath heard thy affliction.
(Gen 16:12) And he will be a wild man; his hand will be against every man, and every man's hand against him; and he shall dwell in the presence of all his brethren.
May the word of God be true and every man a liar!
(Gen 17:20) And as for Ishmael, I have heard thee: Behold, I have blessed him, and will make him fruitful, and will multiply him exceedingly; twelve princes shall he beget, and I will make him a great nation.
(1Ch 1:29) These are their generations: The firstborn of Ishmael, Nebaioth; then Kedar, and Adbeel, and Mibsam,
(1Ch 1:30) Mishma, and Dumah, Massa, Hadad, and Tema,
(1Ch 1:31) Jetur, Naphish, and Kedemah. These are the (12) sons (princes) of Ishmael.
Therefore Ishmael, the father of the Arabic nations was blessed, and made fruitful by the God of Abraham, who multiplied him exceedingly, and made of Him a great nation.
Linguistically, Allah literally means "the god", and many moderate Muslims, as well as many moderate Christians, tend to use this definition, in tandem with the origin of the Arab people, to point out that this god of Islam is the great IAM.
However the god of Islam, Allah, was one of the 360 gods worshiped in the ka’aba in Mecca, and was the chief god for the Quraysh tribe, which was the tribe Muhammad belonged to, and in Muhammad’s campaign against polytheism he chose Allah as the one true God.
Subsequently the god in the Quran IS NOT the God of the Christian and Hebrew scriptures!
The Allah from the Qur’an is very different from the Yahweh of the Bible. For one thing, Allah is a distant, remote being who reveals his will but not himself. It is impossible to know him in a personal way. In his absolute oneness there is unity but not trinity, and because of this lack of relationship, love is not emphasized. For the Muslim, Allah cannot have any associates or relationships with his creations.
Allah is considered to be too holy to have personal relationships with man, but Yahweh is often described as a loving God interested in our personal struggles. Yahweh is also depicted as unchanging and One who assures the salvation of the faithful as well as One who assures a personal relationship with those who seek it.
In the end, according to their doctrine, a Muslem cannot know Allah or even be sure of the consistency of his attributes.
On the other hand, because Yahweh is by nature a triune being his attributes stem from his nature. The eternal relationship within the Trinity promotes love within the Godhead and extends that love to his creation.
What about the Arabic Christians who call the God of the Bible “Allah”?
When the Arabic Christians refer to “Allah” in their translation of the Bible, they believe that “Allah” is the father of Jesus and they believe that “Allah” is triune. Therefore, the Allah of the Arabic Christians cannot be the same Allah of the Muslims!
An Arab Christian may still use the word “Allah” to denote God, but his understanding of that term would be starkly different from a Muslim, for the Christian would recognize that Jesus Christ is God (Allah) whereas the Muslim would never consider that connotation.
Therefore, “Allah” for the Muslim cannot be reconciled with the “Jesus is Allah” of the Arabic Christians. There is still a world of difference between the content of the word (connotation), even if the denotation is the same. Without this very important distinction made when we refer to “Allah” and “God” (Yahweh), a lot of Christians will be confused.
It is this misunderstanding which has given birth to what is commonly referred to as Chisholm or the Chisholmic Movement.
THEREFORE, in answer to the question; "Is Allah the God of Abraham, Issac, and Jacob?"
The answer is, yes and no!
For the Muslim who has returned to his or her roots, and uses the name in reference to the triune God of the bible, the Arabic name Allah speaks of the God of Abraham, Isaac, and Jacob.
For the Muslim who is still rooted in the religion of Islam, Allah is the god whom Muhammad choose from among 360 pagan gods, to be "the god" of the book which he authored, the Quran.
The first-known translation of the Bible into Arabic, which took place in the 9th century, uses the word Allah for God.
In fact, Arab Christians were using the word Allah for God prior to the dawn of Islam, it is important to note however that they were using it in place of Elohim, but not in place of Yahweh (Jehovah - the existing one). That means Allah, to many Arabic Christians, is a generic word for God, but not the personal name of God.
The problem here is that Elohim (Hebrew noun masculine plural) denotes Jehovah as being more than one person, and subsequently, many followers of Islam converted to Christianity do not necessarily hold to the trinitarian, or multi personage doctrine of our faith.
The bottom line however is that it is not the name, in and of itself, that is important, rather the heart of the person using it, and what they profess with their mouths about God (Jehovah), and His divine nature, that truly matters.
It really doesn't matter if you use the name Yahweh, or Theos, or Eilah, or Godt, or Dieu, or Bojh, or Allah, depending on your native tongue, if you are speaking of the Eternal God of Abraham, Isaac, and Jacob when you do so.
Allah the God of Abraham, Isaac & Jacob