Abstract

We present some results on the existence, uniqueness and Hyers–Ulam stability to the solution of an implicit coupled system of impulsive fractional differential equations having Hadamard type fractional derivative. Using a fixed point theorem of Kransnoselskii’s type, the existence and uniqueness results are obtained. Along these lines, different kinds of Hyers–Ulam stability are discussed. An example is given to illustrate the main theorems.

Details

Title
Analysis of coupled systems of implicit impulsive fractional differential equations involving Hadamard derivatives
Author
Riaz, Usman 1 ; Zada, Akbar 1 ; Ali, Zeeshan 1 ; Cui, Yujun 2   VIAFID ORCID Logo  ; Xu, Jiafa 3 

1  Department of Mathematics, University of Peshawar, Peshawar, Pakistan 
2  State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao, P.R. China 
3  School of Mathematical Sciences, Chongqing Normal University, Chongqing, P.R. China 
Pages
1-27
Publication year
2019
Publication date
Jun 2019
Publisher
Springer Nature B.V.
ISSN
1687-1839
e-ISSN
1687-1847
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1186/s13662-019-2163-8
ProQuest document ID
2238049488
Copyright
Advances in Difference Equations is a copyright of Springer, (2019). All Rights Reserved., © 2019. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.