Abstract
Some essential conditions for existence theory and stability analysis to a class of boundary value problems of fractional delay differential equations involving Atangana-Baleanu-Caputo derivative are established. The deserted results are derived by using the Banach contraction and Krasnoselskii's fixed point theorems. Moreover, different kinds of stability theory including Hyers-Ulam, generalized Hyers-Ulam, Hyers-Ulam-Rassias and generalized Hyers-Ulam-Rassias stability are also developed for the problem under consideration. Appropriate examples are given for illustrative purposes.