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":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":"174 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Mathematics and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524700751","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","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.
期刊介绍：
Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.
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