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On Fractional Langevin Equations with Stieltjes Integral Conditions

Author

Listed:
  • Binlin Zhang

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Rafia Majeed

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Mehboob Alam

    (Faculty of Engineering Sciences, GIK Institute, Topi 23640, Pakistan)

Abstract

In this paper, we focus on the study of the implicit FDE involving Stieltjes integral boundary conditions. We first exploit some sufficient conditions to guarantee the existence and uniqueness of solutions for the above problems based on the Banach contraction principle and Schaefer’s fixed point theorem. Then, we present different kinds of stability such as UHS , GUHS , UHRS , and GUHRS by employing the classical techniques. In the end, the main results are demonstrated by two examples.

Suggested Citation

  • Binlin Zhang & Rafia Majeed & Mehboob Alam, 2022. "On Fractional Langevin Equations with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3877-:d:946660
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    References listed on IDEAS

    as
    1. Danfeng Luo & Mehboob Alam & Akbar Zada & Usman Riaz & Zhiguo Luo & Peter Giesl, 2021. "Existence and Stability of Implicit Fractional Differential Equations with Stieltjes Boundary Conditions Involving Hadamard Derivatives," Complexity, Hindawi, vol. 2021, pages 1-36, March.
    2. Jiqiang Jiang & Donal O’Regan & Jiafa Xu & Yujun Cui, 2019. "Positive Solutions for a Hadamard Fractional p -Laplacian Three-Point Boundary Value Problem," Mathematics, MDPI, vol. 7(5), pages 1-20, May.
    3. Shah, Syed Omar & Zada, Akbar, 2019. "Existence, uniqueness and stability of solution to mixed integral dynamic systems with instantaneous and noninstantaneous impulses on time scales," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 202-213.
    4. Alam, Mehboob & Zada, Akbar, 2022. "Implementation of q-calculus on q-integro-differential equation involving anti-periodic boundary conditions with three criteria," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    5. Zada, Akbar & Ali, Wajid & Park, Choonkil, 2019. "Ulam’s type stability of higher order nonlinear delay differential equations via integral inequality of Grönwall-Bellman-Bihari’s type," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 60-65.
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    Cited by:

    1. Rafia Majeed & Binlin Zhang & Mehboob Alam, 2023. "Fractional Langevin Coupled System with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
    2. Wuyang Wang & Khansa Hina Khalid & Akbar Zada & Sana Ben Moussa & Jun Ye, 2023. "q -Fractional Langevin Differential Equation with q -Fractional Integral Conditions," Mathematics, MDPI, vol. 11(9), pages 1-27, May.

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