Краевые задачи для линейного обыкновенного дифференциального уравнения дробного порядка с запаздывающим аргументом

In this paper we obtained the explicit representations of the solutions of Dirichlet and Neumann problems for a linear ordinary differential equation of fractional order with delay. The Green's functions of the problems are constructed. The theorems of existence and uniqueness of solutions of investigated problems are proved. It is proved that the solvability conditions can be violated only a finite number of times.