Rob Christian and Al Fadi discuss the claim that Mohammad is a descendant of Ishmael. They use Muslim sources . First the Quran does not mention that Mohammad is related to Ishmael. According to a book called "History and Knowledge", vol1,pg 269  Al Abbas; Mohammad's uncle, said that Mohammad was a nobody to the Quraish tribe.  Another source is Life of the Prophet by Ibn Kathir vol 1, pg. 51; it says that there is a broken lineage between Adnan and Ishmael. Omar Ibn Al Khattab said that they only carry the lineage as far as Adnan.  So Muslims can not back up the claim.