IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i20p3877-d946660.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/20/3877/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/20/3877/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Rafia Majeed & Binlin Zhang & Mehboob Alam, 2023. "Fractional Langevin Coupled System with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 11(10), pages 1-14, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Alam, Mehboob & Shah, Dildar, 2021. "Hyers–Ulam stability of coupled implicit fractional integro-differential equations with Riemann–Liouville derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Akbar Zada & Shaheen Fatima & Zeeshan Ali & Jiafa Xu & Yujun Cui, 2019. "Stability Results for a Coupled System of Impulsive Fractional Differential Equations," Mathematics, MDPI, vol. 7(10), pages 1-29, October.
    4. Jiafa Xu & Jiqiang Jiang & Donal O’Regan, 2020. "Positive Solutions for a Class of p -Laplacian Hadamard Fractional-Order Three-Point Boundary Value Problems," Mathematics, MDPI, vol. 8(3), pages 1-13, February.
    5. 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).
    6. Usman Riaz & Akbar Zada & Zeeshan Ali & Ioan-Lucian Popa & Shahram Rezapour & Sina Etemad, 2021. "On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    7. Moualkia, Seyfeddine, 2023. "Mathematical analysis of new variant Omicron model driven by Lévy noise and with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    8. 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.
    9. Singh, Ajeet & Shukla, Anurag & Vijayakumar, V. & Udhayakumar, R., 2021. "Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    10. Shuyi Wang & Fanwei Meng, 2021. "Ulam Stability of n -th Order Delay Integro-Differential Equations," Mathematics, MDPI, vol. 9(23), pages 1-17, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3877-:d:946660. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.