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Fractional Langevin Equations with Nonlocal Integral Boundary Conditions

Author

Listed:
  • Ahmed Salem

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

  • Faris Alzahrani

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

  • Lamya Almaghamsi

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    Department of Mathematics, University of Jeddah, Jeddah 41510, Saudi Arabia)

Abstract

In this paper, we investigate a class of nonlinear Langevin equations involving two fractional orders with nonlocal integral and three-point boundary conditions. Using the Banach contraction principle, Krasnoselskii’s and the nonlinear alternative Leray Schauder theorems, the existence and uniqueness results of solutions are proven. The paper was appended examples which illustrate the applicability of the results.

Suggested Citation

  • Ahmed Salem & Faris Alzahrani & Lamya Almaghamsi, 2019. "Fractional Langevin Equations with Nonlocal Integral Boundary Conditions," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:402-:d:228477
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    References listed on IDEAS

    as
    1. Fazli, Hossein & Nieto, Juan J., 2018. "Fractional Langevin equation with anti-periodic boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 332-337.
    2. Bashir Ahmad & Juan J. Nieto, 2010. "Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-10, December.
    3. Ahmad, Bashir & Luca, Rodica, 2018. "Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 516-534.
    4. Ahmad, Bashir & Luca, Rodica, 2017. "Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 378-388.
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    Cited by:

    1. B. Radhakrishnan & T. Sathya, 2022. "Controllability of Hilfer Fractional Langevin Dynamical System with Impulse in an Abstract Weighted Space," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 265-281, October.
    2. Ahmed Salem & Lamya Almaghamsi, 2023. "Solvability of Sequential Fractional Differential Equation at Resonance," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    3. Mieczysław Cichoń & Hussein A. H. Salem & Wafa Shammakh, 2024. "On the Equivalence between Differential and Integral Forms of Caputo-Type Fractional Problems on Hölder Spaces," Mathematics, MDPI, vol. 12(17), pages 1-23, August.

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