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The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm-Liouville Functional Differential Equation

Author

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  • Yanan Li
  • Shurong Sun
  • Zhenlai Han
  • Hongling Lu

Abstract

We study boundary value problems for the following nonlinear fractional Sturm-Liouville functional differential equations involving the Caputo fractional derivative: + , , , , , , , where , denote the Caputo fractional derivatives, is a nonnegative continuous functional defined on , , , , are suitably small, , and , . By means of the Guo-Krasnoselskii fixed point theorem and the fixed point index theorem, some positive solutions are obtained, respectively. As an application, an example is presented to illustrate our main results.

Suggested Citation

  • 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, Hindawi, vol. 2013, pages 1-20, September.
    • Handle: RePEc:hin:jnlaaa:301560
    DOI: 10.1155/2013/301560
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