Analysis of coupled systems of implicit impulsive fractional differential equations involving Hadamard derivatives

Advances in Difference Equations

Usman Riaz¹  Zeeshan Ali¹  Akbar Zada¹  Jiafa Xu²  Yujun Cui³ 

[1] Department of Mathematics, University of Peshawar;School of Mathematical Sciences, Chongqing Normal University;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;

关键词: Hadamard fractional derivative;    Nonlinear implicit impulsive coupled system;    Existence theory;    Hyers–Ulam stability;   

DOI  :  10.1186/s13662-019-2163-8

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown