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The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses

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  • Xianzhen Zhang
  • Zuohua Liu
  • Hui Peng
  • Xianmin Zhang
  • Shiyong Yang

Abstract

Based on some recent works about the general solution of fractional differential equations with instantaneous impulses, a Caputo-Hadamard fractional differential equation with noninstantaneous impulses is studied in this paper. An equivalent integral equation with some undetermined constants is obtained for this fractional order system with noninstantaneous impulses, which means that there is general solution for the impulsive systems. Next, an example is given to illustrate the obtained result.

Suggested Citation

  • Xianzhen Zhang & Zuohua Liu & Hui Peng & Xianmin Zhang & Shiyong Yang, 2017. "The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-11, February.
    • Handle: RePEc:hin:jnlamp:3094173
    DOI: 10.1155/2017/3094173
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