{"title":"利用一种富有想象力的方法来研究基于莫汉德 HPA 的分式纽厄尔-怀特海-西格尔方程","authors":"Sajad Iqbal, Jun Wang","doi":"10.1007/s10665-024-10381-z","DOIUrl":null,"url":null,"abstract":"<p>This study implemented a novel technique to address the common issue of stripe pattern formation in 2D systems known as the time-fractional Newell–Whitehead–Segel problem. The study presents the Mohand transforms and their properties in conformable sense. The proposed solution involved utilizing the homotopy perturbation approach (HPA) and conformable Mohand transform (CMT) to tackle four case studies of the time-fractional Newell–Whitehead–Segel problem. The graphical outcomes produced by the suggested approach resembled the exact solution. The effectiveness of the suggested techniques was demonstrated by presenting precise and analytical data through graphs. Additionally, the results of using the suggested technique for different values of <span>\\(\\alpha \\)</span> were compared, showing that as the value moves from a fractional order to an integer order, the answer becomes more and more similar to the exact solution.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Utilizing an imaginative approach to examine a fractional Newell–Whitehead–Segel equation based on the Mohand HPA\",\"authors\":\"Sajad Iqbal, Jun Wang\",\"doi\":\"10.1007/s10665-024-10381-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This study implemented a novel technique to address the common issue of stripe pattern formation in 2D systems known as the time-fractional Newell–Whitehead–Segel problem. The study presents the Mohand transforms and their properties in conformable sense. The proposed solution involved utilizing the homotopy perturbation approach (HPA) and conformable Mohand transform (CMT) to tackle four case studies of the time-fractional Newell–Whitehead–Segel problem. The graphical outcomes produced by the suggested approach resembled the exact solution. The effectiveness of the suggested techniques was demonstrated by presenting precise and analytical data through graphs. Additionally, the results of using the suggested technique for different values of <span>\\\\(\\\\alpha \\\\)</span> were compared, showing that as the value moves from a fractional order to an integer order, the answer becomes more and more similar to the exact solution.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1007/s10665-024-10381-z\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s10665-024-10381-z","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Utilizing an imaginative approach to examine a fractional Newell–Whitehead–Segel equation based on the Mohand HPA
This study implemented a novel technique to address the common issue of stripe pattern formation in 2D systems known as the time-fractional Newell–Whitehead–Segel problem. The study presents the Mohand transforms and their properties in conformable sense. The proposed solution involved utilizing the homotopy perturbation approach (HPA) and conformable Mohand transform (CMT) to tackle four case studies of the time-fractional Newell–Whitehead–Segel problem. The graphical outcomes produced by the suggested approach resembled the exact solution. The effectiveness of the suggested techniques was demonstrated by presenting precise and analytical data through graphs. Additionally, the results of using the suggested technique for different values of \(\alpha \) were compared, showing that as the value moves from a fractional order to an integer order, the answer becomes more and more similar to the exact solution.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.