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
收藏
页数：14
相关论文
共 50 条
  • [41] Existence theorems and Hyers-Ulam stability for a coupled system of fractional differential equations with p-Laplacian operator
    Hasib Khan
    Yongjin Li
    Wen Chen
    Dumitru Baleanu
    Aziz Khan
    Boundary Value Problems, 2017
  • [42] EXISTENCE THEOREMS AND HYERS-ULAM STABILITY FOR A CLASS OF HYBRID FRACTIONAL DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN OPERATOR
    Khan, Hasib
    Tunc, Cemil
    Chen, Wen
    Khan, Aziz
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2018, 8 (04): : 1211 - 1226
  • [43] Comment for "Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel"
    Li, Xiaoyan
    CHAOS SOLITONS & FRACTALS, 2021, 142
  • [44] Hyers-Ulam and Hyers-Ulam-Aoki-Rassias Stability for Linear Ordinary Differential Equations
    Mohapatra, A. N.
    APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL, 2015, 10 (01): : 149 - 161
  • [45] Hyers-Ulam Stability of Fifth Order Linear Differential Equations
    Bowmiya, S.
    Balasubramanian, G.
    Govindan, Vediyappan
    Donganon, Mana
    Byeon, Haewon
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2024, 17 (04): : 3585 - 3609
  • [46] Hyers-Ulam stability of delay differential equations of first order
    Huang, Jinghao
    Li, Yongjin
    MATHEMATISCHE NACHRICHTEN, 2016, 289 (01) : 60 - 66
  • [47] Hyers-Ulam stability of linear differential equations of first order
    Jung, SM
    APPLIED MATHEMATICS LETTERS, 2004, 17 (10) : 1135 - 1140
  • [48] Hyers-Ulam stability of nth order linear differential equations
    Li, Tongxing
    Zada, Akbar
    Faisal, Shah
    JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (05): : 2070 - 2075
  • [49] Hyers-Ulam stability of linear differential equations of second order
    Li, Yongjin
    Shen, Yan
    APPLIED MATHEMATICS LETTERS, 2010, 23 (03) : 306 - 309
  • [50] ON HYERS-ULAM STABILITY FOR NONLINEAR DIFFERENTIAL EQUATIONS OF NTH ORDER
    Qarawani, Maher Nazmi
    INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2013, 2 (01): : 71 - 78
12345