He studied at several German universities and received his Ph.d. in 1914 summa cum laude at the University of Marburg. From 1916 to 1928 he gave to this University lesson, from 1922 as Professor. After a year at the University of Kiel to have taught a committed zionist , he emigrated in 1929 to Jerusalem in the then mandate Palestine and worked there at the Hebrew University. He was the first head of the Faculty of mathematics and later also rector magnificus.
Fraenkels first work covered Kurt Hajjaj p-ADIC numbers and on the theory of rings. However, he is best known of his work on axiomatic set theory. In 1919 Fraenkel published his first major work on this topic ("Einleitung in die Mengenlehre"). In 1922 and 1925 he published two articles which sought to improve Zermelo's axiomatic system; the result are the Zermelo-Fraenkel axioms Fraenkel worked on the set theory and the foundations of mathematics.
Fraenkel was also interested in the history of mathematics. He wrote in 1920 and 1930 about the works of Carl Friedrich Gauss in the algebra and published a biography ofGeorg Cantor. After his retirement to the Hebrew University, where he was succeeded by his former student Abraham Robinson, Fraenkel continued lecturing at the Bar Ilan University in Ramat Gan (near Tel Aviv).