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Existence and Iterative Method for Some Riemann Fractional Nonlinear Boundary Value Problems

Author

Listed:
  • Imed Bachar

    (Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Habib Mâagli

    (Department of Mathematics, College of Sciences and Arts, King Abdulaziz University, Rabigh Campus, P.O. Box 344, Rabigh 21911, Saudi Arabia
    Analyse Harmonique et Théorie du Potentiel, LR10ES09 Modélisation Mathématique, Faculté des Sciences de Tunis, Université de Tunis El Manar, Tunis 2092, Tunisie)

  • Hassan Eltayeb

    (Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

Abstract

In this paper, we prove the existence and uniqueness of solution for some Riemann–Liouville fractional nonlinear boundary value problems. The positivity of the solution and the monotony of iterations are also considered. Some examples are presented to illustrate the main results. Our results generalize those obtained by Wei et al., (Existence and iterative method for some fourth order nonlinear boundary value problems. Appl. Math. Lett. 2019, 87, 101–107.) to the fractional setting.

Suggested Citation

  • Imed Bachar & Habib Mâagli & Hassan Eltayeb, 2019. "Existence and Iterative Method for Some Riemann Fractional Nonlinear Boundary Value Problems," Mathematics, MDPI, vol. 7(10), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:961-:d:275995
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    References listed on IDEAS

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    1. Chengjun Yuan & Daqing Jiang & Xiaojie Xu, 2009. "Singular Positone and Semipositone Boundary Value Problems of Nonlinear Fractional Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-17, July.
    2. Habib Mâagli & Noureddine Mhadhebi & Noureddine Zeddini, 2013. "Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, February.
    3. Ramzi S. Alsaedi, 2014. "Existence and Global Behavior of Positive Solutions for Some Fourth-Order Boundary Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, March.
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    Cited by:

    1. Ravi P. Agarwal & Petio S. Kelevedjiev, 2020. "On the Solvability of Fourth-Order Two-Point Boundary Value Problems," Mathematics, MDPI, vol. 8(4), pages 1-19, April.

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