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1 < α < 2阶非线性分数阶微分方程解的渐近稳定性
葛富东,寇春海
东华大学
摘要:
主要讨论了一类阶数为1 < α < 2 的非线性分数阶微分方程解的渐近稳定性.这类方程首先被转化为带有分数次积分扰动的常微分方程,进而运用Banach压缩映照原理,建立了一些保证这类方程的解渐近稳定的充分条件,围绕非线性分数阶微分方程的稳定性分析进行了新的尝试.最后通过举例说明该方法的有效性.
关键词:  非线性分数阶微分方程  Banach压缩映照  渐近稳定性
DOI:
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基金项目:
Asymptotic stability of solutions of nonlinear fractional differential equations of order 1 < α < 2
GE Fudong1, KOU Chunhai2
1.College of Information Science and Technology, Donghua University;2.College of Science, Donghua University
Abstract:
This paper is mainly concerned with the asymptotic stability of the solutions of a class of nonlinear fractional differential equations of order 1 < α < 2 in a weighted Banach space. By first converting the nonlinear fractional differential equations to ordinary differential equations with a fractional integral perturbation, our main results are obtained via the Banach contraction mapping principle, which surely provides a new way to the stability analysis of nonlinear fractional differential equations. An application is also introduced to validate the above conclusions.
Key words:  nonlinear fractional differential equations  Banach contraction mapping  asymptotic stability