{"title":"多孔介质流动模型中求解时间分数型广义Burgers-Fisher方程的交替变分迭代Elzaki变换方法","authors":"Jyoti U. Yadav, Twinkle R. Singh","doi":"10.1002/mma.10848","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>In this paper, we have studied the time-fractional generalized Burgers-Fisher equation, which has applications in turbulence modeling, image processing, and biology. A new method called the alternative variational iteration Elzaki transform method (AVIETM) has been used to achieve the results. We employed the proposed method to obtain a solution for the time-fractional generalized Burgers-Fisher equation. The convergence and uniqueness of the solutions for the proposed method have been analyzed and discussed. The validity of the AVIETM is shown by numerical simulation and graphs. The method's accuracy have been shown by comparing the results to exact for various values of the fractional order. The obtained results demonstrate that the proposed AVIETM method is straightforward, highly accurate, and efficient.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9853-9865"},"PeriodicalIF":2.1000,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Alternative Variational Iteration Elzaki Transform Method for Solving Time-Fractional Generalized Burgers-Fisher Equation in Porous Media Flow Modeling\",\"authors\":\"Jyoti U. Yadav, Twinkle R. Singh\",\"doi\":\"10.1002/mma.10848\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>In this paper, we have studied the time-fractional generalized Burgers-Fisher equation, which has applications in turbulence modeling, image processing, and biology. A new method called the alternative variational iteration Elzaki transform method (AVIETM) has been used to achieve the results. We employed the proposed method to obtain a solution for the time-fractional generalized Burgers-Fisher equation. The convergence and uniqueness of the solutions for the proposed method have been analyzed and discussed. The validity of the AVIETM is shown by numerical simulation and graphs. The method's accuracy have been shown by comparing the results to exact for various values of the fractional order. The obtained results demonstrate that the proposed AVIETM method is straightforward, highly accurate, and efficient.</p>\\n </div>\",\"PeriodicalId\":49865,\"journal\":{\"name\":\"Mathematical Methods in the Applied Sciences\",\"volume\":\"48 9\",\"pages\":\"9853-9865\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2025-03-05\",\"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.10848\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10848","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Alternative Variational Iteration Elzaki Transform Method for Solving Time-Fractional Generalized Burgers-Fisher Equation in Porous Media Flow Modeling
In this paper, we have studied the time-fractional generalized Burgers-Fisher equation, which has applications in turbulence modeling, image processing, and biology. A new method called the alternative variational iteration Elzaki transform method (AVIETM) has been used to achieve the results. We employed the proposed method to obtain a solution for the time-fractional generalized Burgers-Fisher equation. The convergence and uniqueness of the solutions for the proposed method have been analyzed and discussed. The validity of the AVIETM is shown by numerical simulation and graphs. The method's accuracy have been shown by comparing the results to exact for various values of the fractional order. The obtained results demonstrate that the proposed AVIETM method is straightforward, highly accurate, and efficient.
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
