Application of Natural Generalized-Laplace Transform and Its Properties

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

Mathematics, 2025, vol. 13, issue 19, 1-21

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).

Keywords: natural generalized Laplace transform; inverse natural generalized-Laplace transform; singular Boussinesq equation; single natural transform; natural generalized-Laplace transform decomposition methods; partial derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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