IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i12p2778-d1175011.html
   My bibliography  Save this article

Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential Equations

Author

Listed:
  • L. Chitra

    (Department of Mathematics, Kandaswami Kandra’s College, Paramathi Velur 638182, Tamil Nadu, India
    These authors contributed equally to this work.)

  • K. Alagesan

    (Department of Mathematics, Kandaswami Kandra’s College, Paramathi Velur 638182, Tamil Nadu, India
    These authors contributed equally to this work.)

  • Vediyappan Govindan

    (Department of Mathematics, Hindustan Institute of Technology and Science, Rajiv Gandhi Salai (OMR), Padur, Kelambakkam, Chennai 603103, Tamil Nadu, India
    These authors contributed equally to this work.)

  • Salman Saleem

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
    These authors contributed equally to this work.)

  • A. Al-Zubaidi

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
    These authors contributed equally to this work.)

  • C. Vimala

    (Department of Mathematics, Periyar Maniammai Institute of Science & Technology, Vallam, Thanjavur 613403, Tamil Nadu, India
    These authors contributed equally to this work.)

Abstract

In this manuscript, we discuss the Tarig transform for homogeneous and non-homogeneous linear differential equations. Using this Tarig integral transform, we resolve higher-order linear differential equations, and we produce the conditions required for Hyers–Ulam stability. This is the first attempt to use the Tarig transform to show that linear and nonlinear differential equations are stable. This study also demonstrates that the Tarig transform method is more effective for analyzing the stability issue for differential equations with constant coefficients. A discussion of applications follows, to illustrate our approach. This research also presents a novel approach to studying the stability of differential equations. Furthermore, this study demonstrates that Tarig transform analysis is more practical for examining stability issues in linear differential equations with constant coefficients. In addition, we examine some applications of linear, nonlinear, and fractional differential equations, by using the Tarig integral transform.

Suggested Citation

  • L. Chitra & K. Alagesan & Vediyappan Govindan & Salman Saleem & A. Al-Zubaidi & C. Vimala, 2023. "Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential Equations," Mathematics, MDPI, vol. 11(12), pages 1-25, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2778-:d:1175011
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/12/2778/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/12/2778/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zada, Akbar & Shah, Omar & Shah, Rahim, 2015. "Hyers–Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 512-518.
    2. Yongjin Li & Yan Shen, 2009. "Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-7, October.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Ginkyu Choi & Soon-Mo Jung & Jaiok Roh, 2019. "Some Properties of Approximate Solutions of Linear Differential Equations," Mathematics, MDPI, vol. 7(9), pages 1-11, September.
    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. Samina & Kamal Shah & Rahmat Ali Khan, 2020. "Stability theory to a coupled system of nonlinear fractional hybrid differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 669-687, June.
    5. Daniela Marian & Sorina Anamaria Ciplea & Nicolaie Lungu, 2022. "Hyers–Ulam Stability of a System of Hyperbolic Partial Differential Equations," Mathematics, MDPI, vol. 10(13), pages 1-9, June.
    6. Onitsuka, Masakazu, 2018. "Hyers–Ulam stability of first-order nonhomogeneous linear difference equations with a constant stepsize," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 143-151.
    7. Naveed Ahmad & Zeeshan Ali & Kamal Shah & Akbar Zada & Ghaus ur Rahman, 2018. "Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations," Complexity, Hindawi, vol. 2018, pages 1-15, February.

    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:11:y:2023:i:12:p:2778-:d:1175011. 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.