Ulam-type stability for a class of implicit fractional differential equations with non-instantaneous integral impulses and boundary condition

Advances in Difference Equations

Yongjin Li¹  Sartaj Ali²  Akbar Zada² 

[1] Department of Mathematics, Sun Yat-sen University, Guangzhou, P.R. China;Department of Mathematics, University of Peshawar, Peshawar, Pakistan

关键词: Caputo fractional derivative;    implicit fractional differential equations;    fractional integral;    non-instantaneous impulses;    Ulam-type stability;    Diaz-Margolis’s fixed point theorem;    26A33;    34A08;    34B27;   

DOI  :  10.1186/s13662-017-1376-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we investigate four different types of Ulam stability, i.e., Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of nonlinear implicit fractional differential equations with non-instantaneous integral impulses and nonlinear integral boundary condition. We also establish certain conditions for the existence and uniqueness of solutions for such a class of fractional differential equations using Caputo fractional derivative. The arguments are based on generalized Diaz-Margolis’s fixed point theorem. We provide two examples, which shows the validity of our main results.

【 授权许可】

CC BY