University of TabrizComputational Methods for Differential Equations2345-39828120200101Algorithm for solving the Cauchy problem for stationary systems of fractional order linear ordinary differential equations212221952610.22034/cmde.2019.9526ENFikretAlievInstitute of Applied Mathematics, Baku State University, Z.Khalilov str, 23, AZ1148, Baku AzerbaijanNihanAlievInstitute of Applied Mathematics, Baku State University, Z.Khalilov str, 23, AZ1148, Baku AzerbaijanNargizSafarovaInstitute of Applied Mathematics, Baku State University, Z.Khalilov str, 23, AZ1148, Baku AzerbaijanNailaVelievaInstitute of Applied Mathematics, Baku State University, Z.Khalilov str, 23, AZ1148, Baku AzerbaijanJournal Article20190719A new simplified analytical formula is given for solving the Cauchy problem for a homogeneous system of fractional order linear differential equations with constant coefficients (SFOLDECC). The matrix exponential function in this formula is re- placed by a Taylor series. Next, an analytical expression of the integral is obtained, with the help of which, for the transition matrix, a relation is obtained that allows one to obtain a solution of the Cauchy problem with high accuracy. The results also apply to the case of inhomogeneous systems with constant perturbations and are illustrated by numerical examples.https://cmde.tabrizu.ac.ir/article_9526_34e7ba013b67fb9e9218892109264c08.pdf