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Existence and stability for a semilinear fractional differential equation with two delays

Abstract In this paper, we are concerned with a class of nonlinear fractional differential equation with delays. By means of the contraction mapping principle, we prove the existence of a unique solution and investigate the continuous dependence of the solution upon the initial data and two types of Ulam stability: Ulam-Hyers and Ulam-Hyers-Rassias ones. Then, we give an example to illustrate the main results.