Stability Analysis of Fractional Nonlinear Dynamic Systems With Order Lying in (1,2)

QI Yong-fang, PENG You-hua

doi:10.13371/j.cnki.chin.q.j.m.2019.02.006

Chinese Quarterly Journal of Mathematics >

2019 , Vol. 34 >Issue 2: 188 - 195

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2019.02.006

Stability Analysis of Fractional Nonlinear Dynamic Systems With Order Lying in (1,2)

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School of Mathematics,Pingxiang University

QI Yong-fang(corresponding author)(1984-), male, native of Pingxiang, a teacher of Pingxiang University, Master's degree, engages in Di®erential theory.

Accepted date: 2018-08-26

Online published: 2020-10-06

Supported by

Supported by the Natural Science Foundation of China(11661065)； Youth Fundation of Pingxiang University；

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Abstract

One new theorem for Caputo fractional derivative and two new theorems for Caputo fractional order systems, when 1 < a < 2, are proposed in this paper. The results have proved to be useful in order to apply the fractional-order extension of Lyapunov direct method, to demonstrate the instability and the stability of many fractional order systems,which can be nonlinear and time varying.

Key words： Stability; Instability; Fractional system; Lyapunov function

Cite this article

QI Yong-fang, PENG You-hua . Stability Analysis of Fractional Nonlinear Dynamic Systems With Order Lying in (1,2)[J]. Chinese Quarterly Journal of Mathematics, 2019 , 34(2) : 188 -195 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.02.006

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