分数阶扩散方程描述中的广义特殊函数

IF 0.3 Q4 MATHEMATICS

Communications in Applied and Industrial Mathematics Pub Date : 2019-01-01 DOI:10.1515/caim-2019-0010

C. Cesarano

{"title":"分数阶扩散方程描述中的广义特殊函数","authors":"C. Cesarano","doi":"10.1515/caim-2019-0010","DOIUrl":null,"url":null,"abstract":"Abstract Starting from the heat equation, we discuss some fractional generalizations of various forms. We propose a method useful for analytic or numerical solutions. By using Hermite polynomials of higher and fractional order, we present some operational techniques to find general solutions of extended form to d'Alembert and Fourier equations. We also show that the solutions of the generalized equations discussed here can be expressed in terms of Hermite-based functions.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"10 1","pages":"31 - 40"},"PeriodicalIF":0.3000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"19","resultStr":"{\"title\":\"Generalized special functions in the description of fractional diffusive equations\",\"authors\":\"C. Cesarano\",\"doi\":\"10.1515/caim-2019-0010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Starting from the heat equation, we discuss some fractional generalizations of various forms. We propose a method useful for analytic or numerical solutions. By using Hermite polynomials of higher and fractional order, we present some operational techniques to find general solutions of extended form to d'Alembert and Fourier equations. We also show that the solutions of the generalized equations discussed here can be expressed in terms of Hermite-based functions.\",\"PeriodicalId\":37903,\"journal\":{\"name\":\"Communications in Applied and Industrial Mathematics\",\"volume\":\"10 1\",\"pages\":\"31 - 40\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"19\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/caim-2019-0010\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/caim-2019-0010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 19

摘要

摘要从热方程出发，讨论了各种形式的分式推广。我们提出了一种适用于解析或数值求解的方法。利用高阶和分数阶的Hermite多项式，我们提出了一些运算技术来寻找达朗贝尔方程和傅立叶方程的扩展形式的一般解。我们还证明了这里讨论的广义方程的解可以用基于Hermite的函数表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Generalized special functions in the description of fractional diffusive equations

Abstract Starting from the heat equation, we discuss some fractional generalizations of various forms. We propose a method useful for analytic or numerical solutions. By using Hermite polynomials of higher and fractional order, we present some operational techniques to find general solutions of extended form to d'Alembert and Fourier equations. We also show that the solutions of the generalized equations discussed here can be expressed in terms of Hermite-based functions.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Communications in Applied and Industrial Mathematics Mathematics-Applied Mathematics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.