Special Affine Fourier Transform on Tempered Distribution and Its Application

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-26 DOI:10.1002/mma.10657

Manish Kumar, Bhawna

{"title":"Special Affine Fourier Transform on Tempered Distribution and Its Application","authors":"Manish Kumar,  Bhawna","doi":"10.1002/mma.10657","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>The main aim of this work is to develop a theoretical framework for generalized pseudo-differential operators involving the special affine Fourier transform (SAFT), associated with a symbol \n<span></span><math>\n <semantics>\n <mrow>\n <mi>δ</mi>\n <mo>(</mo>\n <mi>μ</mi>\n <mo>,</mo>\n <mi>η</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$$ \\delta \\left(\\mu, \\eta \\right) $$</annotation>\n </semantics></math>. Some important properties of the SAFT are established, and it is proved that the product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator. Further, we explore the practical applications of the SAFT in solving generalized partial differential equations, such as the generalized telegraph and wave equations, providing closed-form solutions. Furthermore, graphical visualizations for these solutions are illustrated via MATLAB R2023b.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6092-6102"},"PeriodicalIF":2.1000,"publicationDate":"2025-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10657","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

The main aim of this work is to develop a theoretical framework for generalized pseudo-differential operators involving the special affine Fourier transform (SAFT), associated with a symbol $δ (μ, η)$ . Some important properties of the SAFT are established, and it is proved that the product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator. Further, we explore the practical applications of the SAFT in solving generalized partial differential equations, such as the generalized telegraph and wave equations, providing closed-form solutions. Furthermore, graphical visualizations for these solutions are illustrated via MATLAB R2023b.

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.