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

Firdous A. Shah; Waseem Z. Lone; Kottakkaran Sooppy Nisar; Amany Salah Khalifa; Firdous A. Shah; Waseem Z. Lone; Kottakkaran Sooppy Nisar; Amany Salah Khalifa

doi:10.3934/math.2022111

AIMS Mathematics

2022, Volume 7, Issue 2: 1925-1940. doi: 10.3934/math.2022111

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Research article

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

1.
Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
2.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
3.
Department of Clinical Pathology and Pharmaceutics, College of Pharmacy, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

Received: 05 September 2021 Accepted: 28 October 2021 Published: 04 November 2021
MSC : 35K05, 35L05, 42C20, 83C15

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.
- quadratic-phase Fourier transform,
- differentiation theorem,
- Laplace equation,
- wave equation,
- heat equation
Citation: Firdous A. Shah, Waseem Z. Lone, Kottakkaran Sooppy Nisar, Amany Salah Khalifa. Analytical solutions of generalized differential equations using quadratic-phase Fourier transform[J]. AIMS Mathematics, 2022, 7(2): 1925-1940. doi: 10.3934/math.2022111

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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.

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