M. Arshad, S. Khan, M. Sohail, H. Khan, F. Tchier, M. K. Haidary, M. Nadeem
{"title":"The Solution Comparison of Fractional Heat Transfer and Porous Media Equations Using Analytical Techniques","authors":"M. Arshad, S. Khan, M. Sohail, H. Khan, F. Tchier, M. K. Haidary, M. Nadeem","doi":"10.1134/s0965542524700751","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, the mathematical model of heat and porous media equations being considered in fractional form. The Laplace residual power series method and the Laplace Adomian decomposition technique are used to compare the solutions of the fractional heat transfer and porous media equations. For this reason, a few examples are presented to understand the fractional heat transfer and porous media equations in its more accurate form. The results show the simple and sophisticated procedures of the two proposed analytical approaches, where partial differential equations are considered with fractional derivatives. The outcomes of the described methods demonstrate that they have an accurate algorithm to construct with exceptionally precise cost calculation capabilities. The obtained results are presented through tables and graphs and the approximate results are found in great contact with exact solutions.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524700751","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the mathematical model of heat and porous media equations being considered in fractional form. The Laplace residual power series method and the Laplace Adomian decomposition technique are used to compare the solutions of the fractional heat transfer and porous media equations. For this reason, a few examples are presented to understand the fractional heat transfer and porous media equations in its more accurate form. The results show the simple and sophisticated procedures of the two proposed analytical approaches, where partial differential equations are considered with fractional derivatives. The outcomes of the described methods demonstrate that they have an accurate algorithm to construct with exceptionally precise cost calculation capabilities. The obtained results are presented through tables and graphs and the approximate results are found in great contact with exact solutions.
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