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.

引用

页数：14

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