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Research Article | Open Access

Analytical solutions of generalized differential equations using quadratic-phase Fourier transform

Firdous A. Shah1, Waseem Z. Lone1, Kottakkaran Sooppy Nisar2( ), Amany Salah Khalifa3
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
Department of Clinical Pathology and Pharmaceutics, College of Pharmacy, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
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Abstract

The aim of this study is to obtain the analytical solutions of some prominent differential equations including the generalized Laplace, heat and wave equations by using the quadratic-phase Fourier transform. To facilitate the narrative, we formulate the preliminary results vis-a-vis the differentiation properties of the quadratic-phase Fourier transform. The obtained results are reinforced with illustrative examples.

Keywords

quadratic-phase Fourier transformdifferentiation theoremLaplace equationwave equationheat equation
CLC number: 35K05, 35L05, 42C20, 83C15

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 1925-1940
DOI: 10.3934/math.2022111

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Cite this article:
Shah FA, Lone WZ, Nisar KS, et al. Analytical solutions of generalized differential equations using quadratic-phase Fourier transform. AIMS Mathematics, 2022, 7(2): 1925-1940. https://doi.org/10.3934/math.2022111

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Received: 05 September 2021
Accepted: 28 October 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)