带分布时滞分数阶微分方程非振动解的存在性  

Existence of Nonoscillatory Solutions for Fractional Differential Equations with Distributed Delays

作　　者：赵环环 刘有军 康淑瑰 ZHAO Huanhuan;LIU Youjun;KANG Shugui(School of Mathematics and Statistics,Shanxi Datong University,Datong 037009)

机构地区：[1]山西大同大学数学与统计学院,大同037009

出　　处：《工程数学学报》2022年第4期648-656,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11871314,61803241);山西省自然科学基金(201901D111314)。

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。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.

关 键 词：分数阶 Liouville导数 正负系数 分布时滞 非振动解 

分 类 号：O175.14[理学—数学]