Résumé: This paper is devoted to the study of nonlinear fractional Langevin inte-gro differential equations with boundary conditions. Some effective results concerning the existence and uniqueness are obtained by applying the Banach contraction mapping principle and the Schauder fixed point theorem. An example is presented illustrating the effectiveness of the theoretical results.

Résumé: We offer existence criteria and sufficient conditions, so that the trivial solution of the differential system with several delays of feedback control is asymptotically stable. Here the fixed point technique is a practical method for this purpose. When these results are applied to some special delay mathematics models, some new results are obtained.