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Solvability of Sequential Fractional Differential Equation at Resonance

Author

Listed:
  • Ahmed Salem

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Lamya Almaghamsi

    (Department of Mathematics, College of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia)

Abstract

The sequential fractional differential equations at resonance are introduced subject to three-point boundary conditions. The emerged fractional derivative operators in these equations are based on the Caputo derivative of order that lies between 1 and 2. The vital target of the current contribution is to investigate the existence of a solution for the boundary value problem by using the coincidence degree theory due to Mawhin which is basically depending on the Fredholm operator with index zero and two continuous projectors. An example is given to illustrate the deduced theoretical results.

Suggested Citation

  • Ahmed Salem & Lamya Almaghamsi, 2023. "Solvability of Sequential Fractional Differential Equation at Resonance," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:1044-:d:1072928
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    References listed on IDEAS

    as
    1. Ahmed Salem & Faris Alzahrani & Lamya Almaghamsi, 2019. "Fractional Langevin Equations with Nonlocal Integral Boundary Conditions," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
    2. Ahmed Salem & Kholoud N. Alharbi & Hashim M. Alshehri, 2022. "Fractional Evolution Equations with Infinite Time Delay in Abstract Phase Space," Mathematics, MDPI, vol. 10(8), pages 1-17, April.
    3. Qinghao Zhu & Jianming Qi & Wen-Xiu Ma, 2022. "Exact Solutions of the Nonlinear Space-Time Fractional Partial Differential Symmetric Regularized Long Wave (SRLW) Equation by Employing Two Methods," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-20, May.
    4. Ahmed Salem & Rawia Babusail, 2022. "Finite-Time Stability in Nonhomogeneous Delay Differential Equations of Fractional Hilfer Type," Mathematics, MDPI, vol. 10(9), pages 1-14, May.
    5. Ahmed Salem & Aeshah Al-Dosari & Cristiana J. Silva, 2021. "A Countable System of Fractional Inclusions with Periodic, Almost, and Antiperiodic Boundary Conditions," Complexity, Hindawi, vol. 2021, pages 1-10, June.
    6. Ahmed Salem & Noorah Mshary & Mohammad Alomari, 2022. "Coupled Fixed Point Theorem for the Generalized Langevin Equation with Four-Point and Strip Conditions," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-10, November.
    7. Al-Raeei, Marwan, 2021. "Applying fractional quantum mechanics to systems with electrical screening effects," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    8. Alessandra Jannelli, 2020. "Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    9. Thabet Abdeljawad & Fadila Madjidi & Fahd Jarad & Ndolane Sene, 2019. "On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives," Mathematics, MDPI, vol. 7(10), pages 1-13, October.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Abdelhamid Mohammed Djaouti & Khellaf Ould Melha & Muhammad Amer Latif, 2024. "New Results on the Solvability of Abstract Sequential Caputo Fractional Differential Equations with a Resolvent-Operator Approach and Applications," Mathematics, MDPI, vol. 12(8), pages 1-18, April.

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