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Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems

Author

Listed:
  • Shahram Rezapour

    (Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan
    Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran)

  • Salim Ben Chikh

    (Laboratory of Applied Mathematics, University of Kasdi Merbah Ouargla, Ouargla 30000, Algeria)

  • Abdelkader Amara

    (Laboratory of Applied Mathematics, University of Kasdi Merbah Ouargla, Ouargla 30000, Algeria)

  • Sotiris K. Ntouyas

    (Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
    Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematices, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Jessada Tariboon

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

  • Sina Etemad

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran)

Abstract

In this paper, we studied the existence results for solutions of a new class of the fractional boundary value problem in the Caputo–Hadamard settings. Moreover, boundary conditions of this fractional problem were formulated as the mixed multi-order Hadamard integro-derivative conditions. To prove the main existence results, we applied two well-known techniques in the topological degree and fixed point theories. Finally, we provide two examples to show the compatibility of our theoretical findings.

Suggested Citation

  • Shahram Rezapour & Salim Ben Chikh & Abdelkader Amara & Sotiris K. Ntouyas & Jessada Tariboon & Sina Etemad, 2021. "Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems," Mathematics, MDPI, vol. 9(7), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:719-:d:524494
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    References listed on IDEAS

    as
    1. 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.
    2. Sina Etemad & Sotiris K. Ntouyas & Bashir Ahmad, 2019. "Existence Theory for a Fractional q -Integro-Difference Equation with q -Integral Boundary Conditions of Different Orders," Mathematics, MDPI, vol. 7(8), pages 1-15, July.
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    Cited by:

    1. Nemat Nyamoradi & Sotiris K. Ntouyas & Jessada Tariboon, 2022. "Existence and Uniqueness of Solutions for Fractional Integro-Differential Equations Involving the Hadamard Derivatives," Mathematics, MDPI, vol. 10(17), pages 1-15, August.

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