THERMAL SCIENCE

International Scientific Journal

Ji-Huan He

,

Naveed Anjumd

,

Chun-Hui Hee

,

Abdulrahman Ali Alsolamif

BEYOND LAPLACE AND FOURIER TRANSFORMS: CHALLENGES AND FUTURE PROSPECTS

ABSTRACT
Laplace and Fourier transforms are widely used independently in engineering for linear differential equations including fractional differential equations. Here we introduce a generalized integral transform, which is a generalization of the Fourier transform, Laplace transform, and other transforms, e.g., Sumudu transform, Aboodh transform, Pourreza transform, and Mohand transform, making the new transform much attractive and promising. Its basic properties are elucidated, and its applications to initial value problems and integral equations are illustrated, when coupled with the homotopy perturbation, it can be used for various non-linear problems, opening a new window for non-linear science.
KEYWORDS
laplace transform, Fourier transform, Initial value problems, System of ordinary differential equations, Volterra integral equations
PAPER SUBMITTED: 2023-08-04
PAPER REVISED: 2023-09-15
PAPER ACCEPTED: 2023-10-11
PUBLISHED ONLINE: 2023-10-15
DOI REFERENCE: https://doi.org/10.2298/TSCI230804224H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 6, PAGES [5075 - 5089]
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Beyond Laplace and Fourier transforms: Challenges and future prospects

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