## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 419597, 9 pages.

### Oscillation Behavior for a Class of Differential Equation with Fractional-Order Derivatives

Shouxian Xiang, Zhenlai Han, Ping Zhao, and Ying Sun

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#### Abstract

By using a generalized Riccati transformation technique and an inequality, we establish some oscillation theorems for the fractional differential equation $[a\left(t\right)$ ${\left(p\left(t\right)+q\left(t\right)\left({D}_{-}^{\alpha}x\right)\left(t\right){)}^{\gamma}\right]}^{\mathrm{\prime}}$ − $b(t)f\left({\int}_{t}^{\mathrm{\infty}}\mathrm{\u200d}(s-t{)}^{-\alpha}x(s)ds\right)$ = $0$, for $t\u2a7e{t}_{0}>0$, where ${D}_{-}^{\alpha}x$ is the Liouville right-sided fractional derivative of order $\alpha \in (\mathrm{0,1})$ 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 (Chen, 2012).

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 419597, 9 pages.

**Dates**

First available in Project Euclid: 6 October 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1412606719

**Digital Object Identifier**

doi:10.1155/2014/419597

**Mathematical Reviews number (MathSciNet)**

MR3248857

**Zentralblatt MATH identifier**

07022358

#### Citation

Xiang, Shouxian; Han, Zhenlai; Zhao, Ping; Sun, Ying. Oscillation Behavior for a Class of Differential Equation with Fractional-Order Derivatives. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 419597, 9 pages. doi:10.1155/2014/419597. https://projecteuclid.org/euclid.aaa/1412606719

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