非线性中立型分数阶微分方程的振动准则

Oscillation Criteria for Nonlinear Fractional Neutral Differential Equations

研究了非线性中立型分数阶微分方程D_t~α[a(t)D_t~α(x(t)+p(t)x(τ(t)))]+f(t,x(σ(t)))=0,t≥t_0>0,0<α<1,其中Dtα(·)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.

In this paper,we study the oscillation of fractional neutral differential equation D_t~α[a（t）D_t~α（x（t）＋p（t）x（τ（t）））]＋f（t,x（σ（t）））=0,t≥t0〉0,0〈α〈1,where Dtα（·）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.