带阻尼的非线性强迫分数阶微分方程的区间振动准则

Interval Oscillation Criteria for Forced Nonlinear Fractional Differential Equations with Damping

考虑一类带阻尼的非线性强迫分数阶微分方程的解的振动性D_tα[r（t）ψ（x（t））D_tαx（t）]＋p（t）ψ（x（t））D_tαx（t）＋q（t）f（x（t））=e（t）,t≥t_0〉0,0〈α〈1,其中Dαt（·）定义为关于变量t的修正黎曼-刘维尔导数.通过运用一个广义黎卡提变换,不等式和积分平均技巧,该文建立了此方程的一些新的振动准则.

Abstract： In this paper, we discuss the oscillation of solutions to a class of nonlinear forced fractional dif- ferential equations with damping term D_t~α[r（t）ψ（x（t））D_t~αx（t）]＋p（t）ψ（x（t））D_t~αx（t）＋q（t）f（x（t））=e（t）,t≥t_0〉0,0〈α〈1 ,whereDt^a（·）denotes the modified Riemann-Liouville derivative with respect to the variable t. We establish some new oscillation criteria for the equation by using a generalized Riccati transformation,inequalities and an integration average technique.