论文标题
Cauchy问题，用于分数顺序的普通微分方程的线性系统
Cauchy Problem for a Linear System of Ordinary Differential Equations of the Fractional Order
论文作者
论文摘要
本文研究了具有分数分化操作员dzhrbashyan的常规微分方程的线性系统的初始问题 - 具有恒定系数的nersesyan。证明了正在研究的边界价值问题的解决方案的存在和唯一定理。该解决方案是根据矩阵参数的Mittag-Leffler函数明确构建的。 dzhrbashyan- nersesyan运营商是Riemann-Liouville，Caputo和Miller-Ross分数分化运营商的概括。获得的结果作为特殊情况包含与Riemann（Liouville，Caputo和Miller- Ross derivativess）的最初问题系统的研究有关的结果，调查的初始问题将其推广。
The paper investigates the initial problem for a linear system of ordinary differential equations with the fractional differentiation operator Dzhrbashyan -- Nersesyan with constant coefficients. The existence and uniqueness theorems of the solution of the boundary value problem under 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 special cases contain results related to the study of initial problems for systems of ordinary differential equations with Riemann -- Liouville, Caputo and Miller -- Ross derivativess, and the investigated initial problem generalizes them
