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Existence and Uniqueness of Solutions for Fractional Integro-Differential Equations Involving the Hadamard Derivatives

Author

Listed:
  • Nemat Nyamoradi

    (Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah 67149, Iran)

  • Sotiris K. Ntouyas

    (Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece)

  • 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)

Abstract

In this paper, we study the existence and uniqueness of solutions for the following fractional boundary value problem, consisting of the Hadamard fractional derivative: H D α x ( t ) = A f ( t , x ( t ) ) + ∑ i = 1 k C i H I β i g i ( t , x ( t ) ) , t ∈ ( 1 , e ) , supplemented with fractional Hadamard boundary conditions: H D ξ x ( 1 ) = 0 , H D ξ x ( e ) = a H D α − ξ − 1 2 ( H D ξ x ( t ) ) | t = δ , δ ∈ ( 1 , e ) , where 1 < α ≤ 2 , 0 < ξ ≤ 1 2 , a ∈ ( 0 , ∞ ) , 1 < α − ξ < 2 , 0 < β i < 1 , A , C i , 1 ≤ i ≤ k , are real constants, H D α is the Hadamard fractional derivative of order α and H I β i is the Hadamard fractional integral of order β i . By using some fixed point theorems, existence and uniqueness results are obtained. Finally, an example is given for demonstration.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3068-:d:897642
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    References listed on IDEAS

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    1. 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.
    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.
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