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A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential Equations

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  • Jieming Zhang
  • Chen Yang
  • Chengbo Zhai

Abstract

We establish some sufficient conditions for the existence and uniqueness of positive solutions to a class of initial value problem for impulsive fractional differential equations involving the Caputo fractional derivative. Our analysis relies on a fixed point theorem for mixed monotone operators. Our result can not only guarantee the existence of a unique positive solution but also be applied to construct an iterative scheme for approximating it. An example is given to illustrate our main result.

Suggested Citation

  • Jieming Zhang & Chen Yang & Chengbo Zhai, 2013. "A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-8, November.
    • Handle: RePEc:hin:jnddns:745674
    DOI: 10.1155/2013/745674
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