Topological degree theory and Caputo-Hadamard fractional boundary value problems

被引：36
作者：
Amara, Abdelkader [1 ]
Etemad, Sina [2 ]
Rezapour, Shahram [3 ,4 ,5 ]
机构：
[1] Univ Kasdi Merbah, Lab Appl Math, Ouargla 30000, Algeria
[2] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran
[3] Duy Tan Univ, Inst Res & Dev, Da Nang 550000, Vietnam
[4] Duy Tan Univ, Fac Nat Sci, Da Nang 550000, Vietnam
[5] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期
关键词：
Caputo-Hadamard fractional BVP; Condensing operator; Degree theory; The generalized Dhage's theorem; DIFFERENTIAL-EQUATIONS; EXISTENCE;
D O I：
10.1186/s13662-020-02833-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study two hybrid and non-hybrid fractional boundary value problems via the Caputo-Hadamard type derivatives. We seek the existence criteria for these two problems separately. By utilizing the generalized Dhage's theorem, we derive desired results for an integral structure of solutions for the hybrid problems. Also by considering the special case as a non-hybrid boundary value problem (BVP), we establish other results based on the existing tools in the topological degree theory. In the end of the article, we examine our theoretical results by presenting some numerical examples to show the applicability of the analytical findings.
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收藏
页数：22
相关论文
共 54 条
  • [1] Agarwal R.P., 2006, TOPOLOGICAL DEGREE T
  • [2] Ahmad B, 2010, TOPOL METHOD NONL AN, V35, P295
  • [3] Analyzing transient response of the parallel RCL circuit by using the Caputo-Fabrizio fractional derivative
    Alizadeh, Shahram
    Baleanu, Dumitru
    Rezapour, Shahram
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
  • [4] A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions
    Aljoudi, Shorog
    Ahmad, Bashir
    Nieto, Juan J.
    Alsaedi, Ahmed
    [J]. CHAOS SOLITONS & FRACTALS, 2016, 91 : 39 - 46
  • [5] Existence results for hybrid fractional differential equations with three-point boundary conditions
    Amara, Abdelkader
    [J]. AIMS MATHEMATICS, 2020, 5 (02): : 1074 - 1088
  • [6] Ardjouni A., 2019, Open J. Math. Anal, V3, P62, DOI [10.30538/psrp-oma2019.0033, DOI 10.30538/PSRP-OMA2019.0033]
  • [7] On high order fractional integro-differential equations including the Caputo-Fabrizio derivative
    Aydogan, Melike S.
    Baleanu, Dumitru
    Mousalou, Asef
    Rezapour, Shahram
    [J]. BOUNDARY VALUE PROBLEMS, 2018,
  • [8] On approximate solutions for two higher-order Caputo-Fabrizio fractional integro-differential equations
    Aydogan, S. Melike
    Baleanu, Dumitru
    Mousalou, Asef
    Rezapour, Shahram
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2017,
  • [9] On the new fractional hybrid boundary value problems with three-point integral hybrid conditions
    Baleanu, D.
    Etemad, S.
    Pourrazi, S.
    Rezapour, Sh.
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (01)
  • [10] A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative
    Baleanu, Dumitru
    Mohammadi, Hakimeh
    Rezapour, Shahram
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
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