Oscillation behavior for a class of differential equation with fractional-order derivatives
type: Item
instance of: scholarly article
title: Oscillation behavior for a class of differential equation with fractional-order derivatives
zbMATH Open document ID: 1471.34023
DOI: 10.1155/2014/419597
author: Shouxian Xiang
author: Zhenlai Han
author: Ping Zhao
author: Ying Sun
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: 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 [\textit{D.-X. Chen}, Adv. Difference Equ. 2012, Paper No. 33, 10 p. (2012; Zbl 1291.34007)].
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 7022358
Wikidata QID: Q59037849
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/419597
OpenAlex ID: W2024489601
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description: scientific article; zbMATH DE number 7022358