Existence and Ulam-Hyers stability for Caputo conformable differential equations with four-point integral conditions

被引：17
作者：
Aphithana, Aphirak [1 ]
Ntouyas, Sotiris K. [2 ,3 ]
Tariboon, Jessada [1 ]
机构：
[1] King Mongkuts Univ Technol North Bangkok, Fac Sci Appl, Dept Math, Intelligent & Nonlinear Dynam Innovat Res Ctr, Bangkok, Thailand
[2] Univ Ioannina, Dept Math, Ioannina, Greece
[3] King Abdulaziz Univ, Fac Sci, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, Jeddah, Saudi Arabia
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2019年 / 2019卷 / 1期
关键词：
Existence and uniqueness; Fixed point theorem; Fractional differential equations; Conformable integrals; Conformable derivatives; Ulam-Hyers stability; BOUNDARY-VALUE PROBLEM; POSITIVE SOLUTIONS; DISCRETE;
D O I：
10.1186/s13662-019-2077-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we investigate the existence and uniqueness of solutions for conformable derivatives in the Caputo setting with four-point integral conditions, applying standard fixed point theorems such as Banach contraction mapping principle, Krasnoselskii's fixed point theorem, and Leray-Schauder nonlinear alternative. Further, we present Ulam-Hyers stability results by using direct analysis methods. Different types of Ulam-stability, such as Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability, and generalized Ulam-Hyers-Rassias stability, are studied. Examples which support our theoretical results are also presented.
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页数：17
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共 47 条
  • [1] On multi-fusion solitons induced by inelastic collision for quasi-periodic propagation with nonlinear refractive index and stability analysis
    Abdel-Gawad, H., I
    Tantawy, M.
    Inc, Mustafa
    Yusuf, Abdullahi
    [J]. MODERN PHYSICS LETTERS B, 2018, 32 (29):
  • [2] Functionality of circuit via modern fractional differentiations
    Abro, Kashif Ali
    Memon, Ali Asghar
    Memon, Anwar Ahmed
    [J]. ANALOG INTEGRATED CIRCUITS AND SIGNAL PROCESSING, 2019, 99 (01) : 11 - 21
  • [3] Existence results for coupled nonlinear fractional differential equations equipped with nonlocal coupled flux and multi-point boundary conditions
    Agarwal, Ravi P.
    Ahmad, Bashir
    Garout, Doa'a
    Alsaedi, Ahmed
    [J]. CHAOS SOLITONS & FRACTALS, 2017, 102 : 149 - 161
  • [4] Two fractional derivative inclusion problems via integral boundary condition
    Agarwal, Ravi P.
    Baleanu, Dumitru
    Hedayati, Vahid
    Rezapour, Shahram
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2015, 257 : 205 - 212
  • [5] Ahmad B., 2017, Hadamard-type fractional differential equations, inclusions and inequalities
  • [6] Existence results for sequential fractional integro-differential equations with nonlocal multi-point and strip conditions
    Ahmad, Bashir
    Ntouyas, Sotiris K.
    Agarwal, Ravi P.
    Alsaedi, Ahmed
    [J]. BOUNDARY VALUE PROBLEMS, 2016,
  • [7] A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana-Baleanu fractional derivatives
    Aliyu, Aliyu Isa
    Inc, Mustafa
    Yusuf, Abdullahi
    Baleanu, Dumitru
    [J]. CHAOS SOLITONS & FRACTALS, 2018, 116 : 268 - 277
  • [8] A nonlocal multi-point multi-term fractional boundary value problem with Riemann-Liouville type integral boundary conditions involving two indices
    Alsaedi, Ahmed
    Ntouyas, Sotiris K.
    Agarwal, Ravi P.
    Ahmad, Bashir
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2013,
  • [9] [Anonymous], 1993, ROCZNIK NAUK DYDAKT
  • [10] Aoki T., 1950, J. Math. Soc. Japan, V2, P64, DOI DOI 10.2969/JMSJ/00210064
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