河北师范大学学报—

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刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
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非线性中立型分数阶微分方程的振动准则

河北师范大学数学与信息科学学院, 河北石家庄 050024
DOI： 10.13763/j.cnki.jhebnu.nse.2017.06.002

Oscillation Criteria for Nonlinear Fractional Neutral Differential Equations

HAN Xu, LI Sha, LI Qiaoluan

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摘要/Abstract

摘要：

研究了非线性中立型分数阶微分方程
D_t^α[a（t）D_t^αx（t）+p（t）x（τ（t））]+f（t，x（σ（t）））=0，t≥t₀>0，0<α<1，
其中D_t^α（·）表示关于变元t的修正后的Riemann-Liouville导数.利用降阶法及广义Riccati变换，得到方程一些新的振动准则.

Abstract：

In this paper,we study the oscillation of fractional neutral differential equation
D_t^α[a(t)D_t^αx(t)+p(t)x(τ(t))]+f(t,x(σ(t)))=0,t≥t₀>0,0<α<1,
where D_t^α(·) denotes the modified Riemann-Liouville derivative with respect to the variable t.Some new oscillation criteria for the equation through the reduction of order and generalized Riccati transformation.

关键词

关键词： 振动 ; 分数阶微分方程 ; 修正后的Riemann-Liouville导数

Key words： oscillation ; fractional differential equations ; modified Riemann-Liouville derivative

参考文献 13

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