IDEAS home Printed from https://ideas.repec.org/a/hin/jnijde/8243180.html
   My bibliography  Save this article

Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations

Author

Listed:
  • Junfei Cao
  • Zaitang Huang
  • Gaston M. N’Guérékata

Abstract

This paper is concerned with the existence of asymptotically almost automorphic mild solutions to a class of abstract semilinear fractional differential equations where , is a linear densely defined operator of sectorial type on a complex Banach space and is a bounded linear operator defined on , is an appropriate function defined on phase space, and the fractional derivative is understood in the Riemann-Liouville sense. Combining the fixed point theorem due to Krasnoselskii and a decomposition technique, we prove the existence of asymptotically almost automorphic mild solutions to such problems. Our results generalize and improve some previous results since the (locally) Lipschitz continuity on the nonlinearity is not required. The results obtained are utilized to study the existence of asymptotically almost automorphic mild solutions to a fractional relaxation-oscillation equation.

Suggested Citation

  • Junfei Cao & Zaitang Huang & Gaston M. N’Guérékata, 2018. "Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2018, pages 1-23, August.
    • Handle: RePEc:hin:jnijde:8243180
    DOI: 10.1155/2018/8243180
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJDE/2018/8243180.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/IJDE/2018/8243180.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2018/8243180?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ma, Wangrong & Jin, Maozhu & Liu, Yifeng & Xu, Xiaobo, 2019. "Empirical analysis of fractional differential equations model for relationship between enterprise management and financial performance," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 17-23.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:jnijde:8243180. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.