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Existence Result and Uniqueness for Some Fractional Problem

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  • Guotao Wang

    (School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, China
    College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China
    Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Abdeljabbar Ghanmi

    (Faculté des Sciences de Tunis, Université de Tunis El Manar, Tunis 1060, Tunisia)

  • Samah Horrigue

    (Department of Mathematics, Higher Institute of Applied Science and Technology, University of Monastir, Monastir 5000, Tunisia)

  • Samar Madian

    (Basic Sciences Department, Higher Institute for Engineering and Technology, New Damietta 34517, Egypt)

Abstract

In this article, by the use of the lower and upper solutions method, we prove the existence of a positive solution for a Riemann–Liouville fractional boundary value problem. Furthermore, the uniqueness of the positive solution is given. To demonstrate the serviceability of the main results, some examples are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:516-:d:237595
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    References listed on IDEAS

    as
    1. Chaozhu Hu & Bin Liu & Songfa Xie, 2013. "Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
    2. 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.
    3. Changyou Wang & Haiqiang Zhang & Shu Wang, 2012. "Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-16, October.
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