Algorithm for solving the Cauchy problem for stationary systems of fractional order linear ordinary differential equations

	Algorithm for solving the Cauchy problem for stationary systems of fractional order linear ordinary differential equations
Computational Methods for Differential Equations
مقاله 15، دوره 8، شماره 1، فروردین 2020، صفحه 212-221 اصل مقاله (339.07 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2019.9526
نویسندگان
Fikret Aliev^* ؛ Nihan Aliev؛ Nargiz Safarova؛ Naila Velieva
Institute of Applied Mathematics, Baku State University, Z.Khalilov str, 23, AZ1148, Baku Azerbaijan
چکیده
A 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.
کلیدواژه‌ها
Cauchy problem؛ Linear fractional derivative system؛ Mittag-Leffler function؛ Constant matrix coefficients

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