Properties of solutions for fractional-order linear system with differential equations

AIMS Mathematics

Xindong Zhang¹  Shuo Wang¹  Juan Liu² 

[1] 1. School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang 830017, China;2. College of Big Data Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China;

关键词: linear system;    caputo-fabrizio derivative;    analytical solution;    fractional differential;    fractional integral;   

DOI  :  10.3934/math.2022860

来源: DOAJ

【 摘 要 】

In this paper, we study the analytical solutions of two-dimensional fractional-order linear system $ \mathcal{D}^{\alpha}_{t}X(t) = AX(t) $ described by fractional differential equations, where $ \mathcal{D} $ is the fractional derivative in the Caputo-Fabrizio sense and $ A = (a_{ij})_{2\times2} $ is nonsingular coefficient matrix with $ a_{ij}\in\mathbb{R} $. The analytical solutions of fractional-order linear system will be compared to the solution of classical linear system. Examples are provided to characterize the behavior of the solutions for fractional-order linear system.

【 授权许可】

Unknown