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Advances in Mathematical Physics
Volume 2017, Article ID 3094173, 11 pages
Research Article

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

1School of Chemical and Environmental Engineering, Jiujiang University, Jiujiang, Jiangxi 332005, China
2School of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400044, China
3School of Electronic Engineering, Jiujiang University, Jiujiang, Jiangxi 332005, China

Correspondence should be addressed to Xianmin Zhang; moc.621@m2x6z

Received 25 September 2016; Accepted 22 November 2016; Published 9 February 2017

Academic Editor: Kaliyaperumal Nakkeeran

Copyright © 2017 Xianzhen Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.