Abstract and Applied Analysis

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

Abstract

By using a generalized Riccati transformation technique and an inequality, we establish some oscillation theorems for the fractional differential equation $[a(t)$ ${(p(t)+q(t)({D}_{-}^{\alpha }x)(t){)}^{\gamma }]}^{\mathrm{\prime }}$ − $b(t)f({\int }_{t}^{\mathrm{\infty }}\mathrm{‍}(s-t{)}^{-\alpha }x(s)ds)$ = $0$, 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 (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

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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