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

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

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 obta...

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Main Authors: Xianzhen Zhang, Zuohua Liu, Hui Peng, Xianmin Zhang, Shiyong Yang
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2017/3094173
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spelling doaj-f734a6e1360a4dda90460eda6e8c29302021-07-02T11:51:57ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/30941733094173The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous ImpulsesXianzhen Zhang0Zuohua Liu1Hui Peng2Xianmin Zhang3Shiyong Yang4School of Chemical and Environmental Engineering, Jiujiang University, Jiujiang, Jiangxi 332005, ChinaSchool of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400044, ChinaSchool of Electronic Engineering, Jiujiang University, Jiujiang, Jiangxi 332005, ChinaSchool of Electronic Engineering, Jiujiang University, Jiujiang, Jiangxi 332005, ChinaSchool of Electronic Engineering, Jiujiang University, Jiujiang, Jiangxi 332005, ChinaBased 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.http://dx.doi.org/10.1155/2017/3094173
collection DOAJ
language English
format Article
sources DOAJ
author Xianzhen Zhang
Zuohua Liu
Hui Peng
Xianmin Zhang
Shiyong Yang
spellingShingle Xianzhen Zhang
Zuohua Liu
Hui Peng
Xianmin Zhang
Shiyong Yang
The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses
Advances in Mathematical Physics
author_facet Xianzhen Zhang
Zuohua Liu
Hui Peng
Xianmin Zhang
Shiyong Yang
author_sort Xianzhen Zhang
title The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses
title_short The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses
title_full The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses
title_fullStr The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses
title_full_unstemmed The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses
title_sort general solution of differential equations with caputo-hadamard fractional derivatives and noninstantaneous impulses
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2017-01-01
description 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.
url http://dx.doi.org/10.1155/2017/3094173
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