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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (4): 648-656.doi: 10.3969/j.issn.1005-3085.2022.04.012

• • 上一篇    下一篇

带分布时滞分数阶微分方程非振动解的存在性

赵环环,   刘有军,   康淑瑰   

  1. 山西大同大学数学与统计学院，大同 037009
  • 出版日期:2022-08-15 发布日期:2022-10-15
  • 通讯作者: 刘有军 E-mail: lyj9791@126.com
  • 基金资助:
    国家自然科学基金 (11871314; 61803241)；山西省自然科学基金 (201901D111314).

Existence of Nonoscillatory Solutions for Fractional Differential Equations with Distributed Delays

ZHAO Huanhuan,   LIU Youjun,   KANG Shugui   

  1. School of Mathematics and Statistics, Shanxi Datong University, Datong 037009
  • Online:2022-08-15 Published:2022-10-15
  • Contact: Y. Liu. E-mail address: lyj9791@126.com
  • Supported by:
    The National Natural Science Foundation of China (11871314; 61803241); the Natural Sciences Foundation of Shanxi Province (201901D111314).

PDF (PC)

115

摘要：

研究了一类中立型部分带有分布时滞且具有正负系数的分数阶微分方程，利用 Banach 压缩映像原理，通过克服算子构造和不等式放缩技巧，得到了方程有界的非振动解存在的充分条件，将其系数的适用范围拓展成不等于 1 和 $-1$ 的实数，并通过算例验证了相关结果。

关键词: 分数阶, Liouville 导数, 正负系数, 分布时滞, 非振动解

Abstract:

A class of neutral fractional differential equations with  distributed delays and positive and negative coefficients are investigated. Using the Banach contraction mapping principle, by overcoming the operator construction and inequality scaling techniques, the sufficient conditions for the existence of bounded nonoscillatory solutions of the equations is obtained. Especially, the applicable range of these coefficients is extended to real numbers that are not equal to 1 and $-1$, the relevant results are verified by some examples.

Key words: fractional differential equation, Liouville derivative, positive and negative coefficients, distributed delays, nonoscillatory solutions

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