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Successive iterations and positive extremal solutions for a Hadamard type fractional integro-differential equations on infinite domain

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  • Pei, Ke
  • Wang, Guotao
  • Sun, Yanyan

Abstract

A Hadamard type fractional integro-differential equation on infinite intervals is considered. By using monotone iterative technique, we not only get the existence of positive solutions, but also seek the positive minimal and maximal solutions and get two explicit monotone iterative sequences which converge to the extremal solutions. At last, to illustrative the main result, an example is also discussed.

Suggested Citation

  • Pei, Ke & Wang, Guotao & Sun, Yanyan, 2017. "Successive iterations and positive extremal solutions for a Hadamard type fractional integro-differential equations on infinite domain," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 158-168.
    • Handle: RePEc:eee:apmaco:v:312:y:2017:i:c:p:158-168
    DOI: 10.1016/j.amc.2017.05.056
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    References listed on IDEAS

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    1. Almeida, Ricardo & Torres, Delfim F.M., 2015. "Computing Hadamard type operators of variable fractional order," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 74-88.
    2. Aljoudi, Shorog & Ahmad, Bashir & Nieto, Juan J. & Alsaedi, Ahmed, 2016. "A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 39-46.
    3. Ma, Qinghua & Wang, Rongnian & Wang, Junwei & Ma, Yicheng, 2015. "Qualitative analysis for solutions of a certain more generalized two-dimensional fractional differential system with Hadamard derivative," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 436-445.
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    Cited by:

    1. Cai, Ruiyang & Ge, Fudong & Chen, YangQuan & Kou, Chunhai, 2019. "Regional observability for Hadamard-Caputo time fractional distributed parameter systems," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 190-202.
    2. Fang Wang & Lishan Liu & Yonghong Wu & Yumei Zou, 2019. "Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p -Laplacian Operator," Complexity, Hindawi, vol. 2019, pages 1-21, October.
    3. Guotao Wang & Abdeljabbar Ghanmi & Samah Horrigue & Samar Madian, 2019. "Existence Result and Uniqueness for Some Fractional Problem," Mathematics, MDPI, vol. 7(6), pages 1-12, June.
    4. Jiqiang Jiang & Donal O’Regan & Jiafa Xu & Yujun Cui, 2019. "Positive Solutions for a Hadamard Fractional p -Laplacian Three-Point Boundary Value Problem," Mathematics, MDPI, vol. 7(5), pages 1-20, May.
    5. Wang, Guotao & Qin, Jianfang & Zhang, Lihong & Baleanu, Dumitru, 2020. "Explicit iteration to a nonlinear fractional Langevin equation with non-separated integro-differential strip-multi-point boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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