Cauchy Problem for a Linear System of Ordinary Differential Equations of the Fractional Order

We investigate the initial problem for a linear system of ordinary differential equations with constant coefficients and with the Dzhrbashyan-Nersesyan fractional differentiation operator. The existence and uniqueness theorems of the solution of the boundary value problem under the study are proved. The solution is constructed explicitly in terms of the Mittag-Leffler function of the matrix argument. The Dzhrbashyan-Nersesyan operator is a generalization of the Riemann-Liouville, Caputo and Miller-Ross fractional differentiation operators. The obtained results as particular cases contain the results related to the study of initial problems for the systems of ordinary differential equations with Riemann-Liouville, Caputo and Miller-Ross derivatives and the investigated initial problem that generalizes them.