IDEAS home Printed from https://ideas.repec.org/a/hin/jnlaaa/390543.html

Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations

Author

Listed:
  • Yige Zhao
  • Shurong Sun
  • Zhenlai Han
  • Qiuping Li

Abstract

We study the existence of positive solutions for the boundary value problem of nonlinear fractional differential equations ð · ð ›¼ 0 + ð ‘¢ ( ð ‘¡ ) + 𠜆 ð ‘“ ( ð ‘¢ ( ð ‘¡ ) ) = 0 , 0 < ð ‘¡ < 1 , ð ‘¢ ( 0 ) = ð ‘¢ ( 1 ) = ð ‘¢ ′ ( 0 ) = 0 , where 2 < ð ›¼ ≤ 3 is a real number, ð · ð ›¼ 0 + is the Riemann-Liouville fractional derivative, 𠜆 is a positive parameter, and ð ‘“ ∶ ( 0 , + ∞ ) → ( 0 , + ∞ ) is continuous. By the properties of the Green function and Guo-Krasnosel'skii fixed point theorem on cones, the eigenvalue intervals of the nonlinear fractional differential equation boundary value problem are considered, some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established. As an application, some examples are presented to illustrate the main results.

Suggested Citation

  • Yige Zhao & Shurong Sun & Zhenlai Han & Qiuping Li, 2011. "Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-16, December.
    • Handle: RePEc:hin:jnlaaa:390543
    DOI: 10.1155/2011/390543
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/AAA/2011/390543.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/AAA/2011/390543.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2011/390543?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. Kui Liu & Michal Fečkan & D. O’Regan & JinRong Wang, 2019. "Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    2. Habib Mâagli & Noureddine Mhadhebi & Noureddine Zeddini, 2013. "Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Lihong Zhang & Bashir Ahmad & Guotao Wang & Ravi P. Agarwal & Maryem Al-Yami & Wafa Shammakh, 2013. "Nonlocal Integrodifferential Boundary Value Problem for Nonlinear Fractional Differential Equations on an Unbounded Domain," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Imed Bachar & Habib Mâagli, 2014. "Existence and Global Asymptotic Behavior of Positive Solutions for Nonlinear Fractional Dirichlet Problems on the Half‐Line," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Ali Yakar & Mehmet Emir Koksal, 2012. "Existence Results for Solutions of Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Xinguang Zhang & Lishan Liu & Benchawan Wiwatanapataphee & Yonghong Wu, 2012. "Positive Solutions of Eigenvalue Problems for a Class of Fractional Differential Equations with Derivatives," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Wenning Liu & Xingjie Yan & Wei Qi, 2014. "Positive Solutions for Coupled Nonlinear Fractional Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    8. Habib Mâagli & Noureddine Mhadhebi & Noureddine Zeddini, 2014. "Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    9. Yuanyuan Pan & Zhenlai Han & Shurong Sun & Yige Zhao, 2012. "The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    10. Qiuping Li & Shurong Sun & Ping Zhao & Zhenlai Han, 2012. "Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    11. Xingqiu Zhang & Lin Wang, 2012. "Nontrivial Solutions for a Class of Fractional Differential Equations with Integral Boundary Conditions and a Parameter in a Banach Space with Lattice," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    12. Liping Wang & Zongfu Zhou & Hui Zhou, 2014. "Positive Solutions for Singular p‐Laplacian Fractional Differential System with Integral Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    13. Guotao Wang & Bashir Ahmad & Lihong Zhang, 2012. "A Coupled System of Nonlinear Fractional Differential Equations with Multipoint Fractional Boundary Conditions on an Unbounded Domain," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    14. Yanan Li & Shurong Sun & Zhenlai Han & Hongling Lu, 2013. "The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm‐Liouville Functional Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

    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:jnlaaa:390543. 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.