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Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators

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  • Dongyuan Liu
  • Zigen Ouyang
  • Huilan Wang

Abstract

We consider the following state dependent boundary-value problem , ; , where is the standard Riemann-Liouville fractional derivative of order , , , , the function is defined as , and the function is defined as , are continuous on and , . Using Banach contraction mapping principle and Leray-Schauder continuation principle, we obtain some sufficient conditions for the existence and uniqueness of the positive solutions for the above fractional order differential equations, which extend some references.

Suggested Citation

  • Dongyuan Liu & Zigen Ouyang & Huilan Wang, 2015. "Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-11, January.
    • Handle: RePEc:hin:jnlaaa:263748
    DOI: 10.1155/2015/263748
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