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Oscillation behavior for a class of differential equation with fractional-order derivatives. (English) Zbl 1471.34023

Summary: By using a generalized Riccati transformation technique and an inequality, we establish some oscillation theorems for the fractional differential equation \([a \left(t\right)\left(p \left(t\right) + q \left(t\right) \left(D_-^\alpha x\right) \left(t\right))^\gamma\right]' -b(t) f \left(\int_t^{\infty} (s - t)^{- \alpha} x(s) d s\right)=0\), for \(t \geqslant t_0 > 0\), where \(D_-^\alpha x\) is the Liouville right-sided fractional derivative of order \(\alpha \in(0,1)\) of \(x\) and \(\gamma\) is a quotient of odd positive integers. The results in this paper extend and improve the results given in the literatures [D.-X. Chen, Adv. Difference Equ. 2012, Paper No. 33, 10 p. (2012; Zbl 1291.34007)].

MSC:

34A08 Fractional ordinary differential equations

Citations:

Zbl 1291.34007
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References:

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