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

Document Type : Research Paper

Authors

Institute of Applied Mathematics, Baku State University, Z.Khalilov str, 23, AZ1148, Baku Azerbaijan

Abstract

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.

Keywords


Volume 8, Issue 1
January 2020
Pages 212-221
  • Receive Date: 19 July 2019
  • Revise Date: 14 November 2019
  • Accept Date: 14 November 2019
  • First Publish Date: 01 January 2020