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

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  • Shouxian Xiang
  • Zhenlai Han
  • Ping Zhao
  • Ying Sun

Abstract

By using a generalized Riccati transformation technique and an inequality, we establish some oscillation theorems for the fractional differential equation [a(t)pt+qtD-αxt) γ′ − b(t)f∫t∞ (s-t) -αx(s)ds = 0, for t⩾t0 > 0, where D-αx is the Liouville right‐sided fractional derivative of order α ∈ (0,1) of x and γ is a quotient of odd positive integers. The results in this paper extend and improve the results given in the literatures (Chen, 2012).

Suggested Citation

  • Shouxian Xiang & Zhenlai Han & Ping Zhao & Ying Sun, 2014. "Oscillation Behavior for a Class of Differential Equation with Fractional‐Order Derivatives," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:419597
    DOI: 10.1155/2014/419597
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    References listed on IDEAS

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    1. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
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