Ulam–Hyers–Mittag-Leffler stability for ψ-Hilfer fractional-order delay differential equations

被引：0
作者：
Kui Liu
JinRong Wang
Donal O’Regan
机构：
[1] Guizhou Institute of Technology,College of Science
[2] Guizhou University,Department of Mathematics
[3] Qufu Normal University,School of Mathematical Sciences
[4] National University of Ireland,School of Mathematics, Statistics and Applied Mathematics
来源：
Advances in Difference Equations | / 2019卷
关键词：
-Hilfer fractional-order delay differential equations; Solutions; Existence; Stability;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we present results on the existence, uniqueness, and Ulam–Hyers–Mittag-Leffler stability of solutions to a class of ψ-Hilfer fractional-order delay differential equations. We use the Picard operator method and a generalized Gronwall inequality involved in a ψ-Riemann–Liouville fractional integral. Finally, we give two examples to illustrate our main theorems.
引用
收藏
相关论文
共 87 条
[1]  
Abbas S.(2015)New stability results for partial fractional differential inclusions with not instantaneous impulses Fract. Calc. Appl. Anal. 18 172-191
[2]  
Benchohra M.(2015)Uniqueness and Ulam stabilities results for partial fractional differential equations with not instantaneous impulses Appl. Math. Comput. 257 190-198
[3]  
Darwish M.A.(2018)Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations Appl. Math. Comput. 324 254-265
[4]  
Abbas S.(2018)Iterative learning control with pulse compensation for fractional differential equations Math. Slovaca 68 563-574
[5]  
Benchohra M.(2018)Topological structure of the solution set for fractional non-instantaneous impulsive evolution inclusions J. Fixed Point Theory Appl. 20 5003-5014
[6]  
Li M.(2018)Existence and numerical solutions of a coupled system of integral BVP for fractional differential equations Adv. Differ. Equ. 2018 642-663
[7]  
Wang J.(2018)Learning formation control for fractional-order multi-agent systems Math. Methods Appl. Sci. 41 481-489
[8]  
Liu S.(2018)Stable manifolds for some fractional differential equations Nonlinear Anal., Model. Control 23 73-79
[9]  
Wang J.(2018)Numerical analysis for a class of Navier–Stokes equations with time fractional derivatives Appl. Math. Comput. 336 3599-3605
[10]  
Zhou Y.(2016)Local and global existence of mild solutions for a class of nonlinear fractional reaction–diffusion equation with delay Appl. Math. Lett. 61 1420-1433
123456789