Abstract: By using Leray-Schauder degree theory and Banach contraction mapping principle, we studied the existence and uniqueness of solutions for boundary value problems of conformable fractional delay differential equations when the nonlinear term satisfied the growth condition and the Lipschitz condition, we obtained the results of existence and uniqueness of solution for the boundary value problem respectively, and gave an example to illustrate the applicability of the obtained results.

Key words: conformable fractional derivative, delay, boundary value problem, Leray-Schauder degree theory, Banach contraction mapping principle