{"title":"利用半解析技术研究分数阶考希反应扩散方程的分形视图和收敛性","authors":"H.M. Younas , Kousar Yousaf , Imran Siddique , Shaukat Iqbal","doi":"10.1016/j.padiff.2024.100974","DOIUrl":null,"url":null,"abstract":"<div><div>This article solves time-fractional order Cauchy reaction-diffusion equations in approximation using the Optimal Homotopy Asymptotic Method (OHAM).The exact solutions and approximate third-order results achieved using OHAM are compared. It has been noted that for partial time order Cauchy equations for reaction-diffusion, OHAM findings exhibit a substantial convergence rate. Plotting the outcomes of the solutions and tabulating the relative errors are done. In order to find the mentioned solutions Mathematica has been used.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100974"},"PeriodicalIF":0.0000,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fractal-view and convergence of fractional order cauchy reaction-diffusion equations using semi-analytical technique\",\"authors\":\"H.M. Younas , Kousar Yousaf , Imran Siddique , Shaukat Iqbal\",\"doi\":\"10.1016/j.padiff.2024.100974\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This article solves time-fractional order Cauchy reaction-diffusion equations in approximation using the Optimal Homotopy Asymptotic Method (OHAM).The exact solutions and approximate third-order results achieved using OHAM are compared. It has been noted that for partial time order Cauchy equations for reaction-diffusion, OHAM findings exhibit a substantial convergence rate. Plotting the outcomes of the solutions and tabulating the relative errors are done. In order to find the mentioned solutions Mathematica has been used.</div></div>\",\"PeriodicalId\":34531,\"journal\":{\"name\":\"Partial Differential Equations in Applied Mathematics\",\"volume\":\"12 \",\"pages\":\"Article 100974\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Partial Differential Equations in Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2666818124003607\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Partial Differential Equations in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666818124003607","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Fractal-view and convergence of fractional order cauchy reaction-diffusion equations using semi-analytical technique
This article solves time-fractional order Cauchy reaction-diffusion equations in approximation using the Optimal Homotopy Asymptotic Method (OHAM).The exact solutions and approximate third-order results achieved using OHAM are compared. It has been noted that for partial time order Cauchy equations for reaction-diffusion, OHAM findings exhibit a substantial convergence rate. Plotting the outcomes of the solutions and tabulating the relative errors are done. In order to find the mentioned solutions Mathematica has been used.