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Existence of Solutions for Riemann‐Liouville Fractional Boundary Value Problem

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Listed:
  • Wenzhe Xie
  • Jing Xiao
  • Zhiguo Luo

Abstract

By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann‐Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under the classical Nagumo conditions. Also, some results concerning Riemann‐Liouville fractional derivative at extreme points are established with weaker hypotheses, which improve some works in Al‐Refai (2012). As applications, an example is presented to illustrate our main results.

Suggested Citation

  • Wenzhe Xie & Jing Xiao & Zhiguo Luo, 2014. "Existence of Solutions for Riemann‐Liouville Fractional Boundary Value Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:540351
    DOI: 10.1155/2014/540351
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    References listed on IDEAS

    as
    1. Jing Chen & X. H. Tang, 2012. "Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Jing Chen & X. H. Tang, 2012. "Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-21, January.
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