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Article

Application of Natural Generalized-Laplace Transform and Its Properties

Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Mathematics 2025, 13(19), 3194; https://doi.org/10.3390/math13193194
Submission received: 25 August 2025 / Revised: 26 September 2025 / Accepted: 1 October 2025 / Published: 5 October 2025
(This article belongs to the Special Issue Special Functions with Applications)

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 natural generalized Laplace transform; inverse natural generalized-Laplace transform; singular Boussinesq equation; single natural transform; natural generalized-Laplace transform decomposition methods; partial derivative

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MDPI and ACS Style

Eltayeb, H. Application of Natural Generalized-Laplace Transform and Its Properties. Mathematics 2025, 13, 3194. https://doi.org/10.3390/math13193194

AMA Style

Eltayeb H. Application of Natural Generalized-Laplace Transform and Its Properties. Mathematics. 2025; 13(19):3194. https://doi.org/10.3390/math13193194

Chicago/Turabian Style

Eltayeb, Hassan. 2025. "Application of Natural Generalized-Laplace Transform and Its Properties" Mathematics 13, no. 19: 3194. https://doi.org/10.3390/math13193194

APA Style

Eltayeb, H. (2025). Application of Natural Generalized-Laplace Transform and Its Properties. Mathematics, 13(19), 3194. https://doi.org/10.3390/math13193194

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