@article{Huang2022, 
author = {Hui Huang and Kaihong Zhao and Xiuduo Liu},
title = {On solvability of BVP for a coupled Hadamard fractional systems involving fractional derivative impulses},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {10},
pages = {19221-19236},
keywords = {coupled Hadamard fractional system, boundary value problem, solvability, fractional derivative impulse, nonlinear alternative of Leray-Schauder},
url = {https://www.sciopen.com/article/10.3934/math.20221055},
doi = {10.3934/math.20221055},
abstract = {Hadamard fractional calculus is one of the most important fractional calculus theories. Compared with a single Hadamard fractional order equation, Hadamard fractional differential equations have a more complex structure and a wide range of applications. It is difficult and challenging to study the dynamic behavior of Hadamard fractional differential equations. This manuscript mainly deals with the boundary value problem (BVP) of a nonlinear coupled Hadamard fractional system involving fractional derivative impulses. By applying nonlinear alternative of Leray-Schauder, we find some new conditions for the existence of solutions to this nonlinear coupled Hadamard fractional system. Our findings reveal that the impulsive function and its impulsive point have a great influence on the existence of the solution. As an application, we discuss an interesting example to verify the correctness and validity of our results.}
}