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Application of Natural Generalized-Laplace Transform and Its Properties

Author

Listed:
  • Hassan Eltayeb

    (Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

Abstract

In this work, we combine the Natural Transform and generalized-Laplace Transform into a new transform called, the Natural Generalized-Laplace Transform, (NGLT) and some of its properties are provided. Moreover, the existence condition, convolution theorem, periodic theorem, and non-constant coefficient partial derivatives are proved with some details. The (NGLT) is applied to gain the solutions of linear telegraph and partial integro-differential equations. Also, we obtained the solution of the singular one-dimensional Boussinesq equation by employing the Natural Generalized-Laplace Transform Decomposition Method, (NGLTDM).

Suggested Citation

  • Hassan Eltayeb, 2025. "Application of Natural Generalized-Laplace Transform and Its Properties," Mathematics, MDPI, vol. 13(19), pages 1-21, October.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:19:p:3194-:d:1765367
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    References listed on IDEAS

    as
    1. Kholoud Saad Albalawi & Ibtehal Alazman & Jyoti Geetesh Prasad & Pranay Goswami, 2023. "Analytical Solution of the Local Fractional KdV Equation," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    2. Hassan Eltayeb, 2013. "Note on Relation between Double Laplace Transform and Double Differential Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, June.
    3. Hassan Eltayeb & Adem Kiliçman, 2013. "A Note on Double Laplace Transform and Telegraphic Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Hassan Eltayeb, 2013. "Note on Relation between Double Laplace Transform and Double Differential Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Hwajoon Kim, 2017. "The Intrinsic Structure and Properties of Laplace-Typed Integral Transforms," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-8, June.
    6. Hassan Eltayeb & Adem Kiliçman, 2013. "A Note on Double Laplace Transform and Telegraphic Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, February.
    Full references (including those not matched with items on IDEAS)

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