Hyers-Ulam Stability and Existence of Solutions for Differential Equations with Caputo-Fabrizio Fractional Derivative

被引：40
|
作者：
Liu, Kui [1 ]
Feckan, Michal [2 ,3 ]
O'Regan, D. [4 ]
Wang, JinRong [1 ,5 ]
机构：
[1] Guizhou Univ, Dept Math, Guiyang 550025, Guizhou, Peoples R China
[2] Comenius Univ, Fac Math Phys & Informat, Dept Math Anal & Numer Math, Bratislava 84248, Slovakia
[3] Slovak Acad Sci, Math Inst, Stefanikova 49, Bratislava 81473, Slovakia
[4] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway H91 TK33, Ireland
[5] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Peoples R China
来源：
MATHEMATICS | 2019年 / 7卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Caputo-Fabrizio fractional differential equations; Hyers-Ulam stability; MULTIPLE POSITIVE SOLUTIONS; SYSTEM MODEL;
D O I：
10.3390/math7040333
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the Hyers-Ulam stability of linear Caputo-Fabrizio fractional differential equation is established using the Laplace transform method. We also derive a generalized Hyers-Ulam stability result via the Gronwall inequality. In addition, we establish existence and uniqueness of solutions for nonlinear Caputo-Fabrizio fractional differential equations using the generalized Banach fixed point theorem and Schaefer's fixed point theorem. Finally, two examples are given to illustrate our main results.
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页数：14
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