Existence and Stability of a Caputo Variable-Order Boundary Value Problem

被引：10
|
作者：
Benkerrouche, Amar [1 ]
Souid, Mohammed Said [2 ]
Chandok, Sumit [3 ]
Hakem, Ali [1 ]
机构：
[1] Univ Djillali Liabes Sidi Bel Abbes, Lab ACEDP, Sidi Bel Abbes, Algeria
[2] Univ Tiaret, Dept Econ Sci, Tiaret, Algeria
[3] Thapar Inst Engn & Technol, Sch Math, Patiala 147004, Punjab, India
来源：
JOURNAL OF MATHEMATICS | 2021年 / 2021卷
关键词：
FRACTIONAL DIFFERENTIAL-EQUATIONS; DERIVATIVES; UNIQUENESS;
D O I：
10.1155/2021/7967880
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this study, we investigate the existence of a solution to the boundary value problem (BVP) of variable-order Caputo-type fractional differential equation by converting it into an equivalent standard Caputo (BVP) of the fractional constant order with the help of the generalized intervals and the piecewise constant functions. All our results in this study are proved by using Darbo's fixed-point theorem and the Ulam-Hyers (UH) stability definition. A numerical example is given at the end to support and validate the potentiality of our obtained results.
引用
收藏
页数：16
相关论文
共 50 条
  • [41] Numerical algorithm for the variable-order Caputo fractional functional differential equation
    A. H. Bhrawy
    M. A. Zaky
    Nonlinear Dynamics, 2016, 85 : 1815 - 1823
  • [42] Numerical algorithm for the variable-order Caputo fractional functional differential equation
    Bhrawy, A. H.
    Zaky, M. A.
    NONLINEAR DYNAMICS, 2016, 85 (03) : 1815 - 1823
  • [43] Existence and uniqueness results for a nonlinear Caputo fractional boundary value problem on a star graph
    Mehandiratta, Vaibhav
    Mehra, Mani
    Leugering, Guenter
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 477 (02) : 1243 - 1264
  • [44] EXISTENCE OF WEAK SOLUTIONS FOR ψ-CAPUTO FRACTIONAL BOUNDARY VALUE PROBLEM VIA VARIATIONAL METHODS
    Khaliq, Adnan
    Rehman, Mujeeb Ur
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2021, 11 (04): : 1768 - 1778
  • [45] Existence results of sequential fractional Caputo sum-difference boundary value problem
    Metpattarahiran, Chanisara
    Linitda, Thitiporn
    Sitthiwirattham, Thanin
    AIMS MATHEMATICS, 2022, 7 (08): : 15120 - 15137
  • [46] UNIQUENESS OF SOLUTIONS TO INITIAL VALUE PROBLEM OF FRACTIONAL DIFFERENTIAL EQUATIONS OF VARIABLE-ORDER
    An, Jiahui
    Chen, Pengyu
    DYNAMIC SYSTEMS AND APPLICATIONS, 2019, 28 (03): : 607 - 623
  • [47] Existence of solutions to a discrete fourth order boundary value problem
    Graef, John R.
    Heidarkhani, Shapour
    Kong, Lingju
    Wang, Min
    JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2018, 24 (06) : 849 - 858
  • [48] Existence results for perturbed boundary value problem with fractional order
    Wanassi, Om Kalthoum
    Toumi, Faten
    RICERCHE DI MATEMATICA, 2024, 73 (03) : 1367 - 1383
  • [49] EXISTENCE AND UNIQUENESS OF SOLUTIONS OF SECOND ORDER BOUNDARY VALUE PROBLEM
    BAILEY, P
    SHAMPINE, LF
    WALTMAN, P
    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 72 (1P1) : 96 - &
  • [50] EXISTENCE OF SOLUTIONS OF A NONLINEAR THIRD ORDER BOUNDARY VALUE PROBLEM
    Guezane-Lakoud, Assia
    Frioui, Assia
    FIXED POINT THEORY, 2012, 13 (02): : 501 - 506
12345