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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
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    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)

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