{"title":"带有Caputo和Caputo- fabrizio导数的分数阶Fokker-Planck方程分析","authors":"Süleyman Çetinkaya, A. Demir, D. Baleanu","doi":"10.52846/ami.v48i1.1473","DOIUrl":null,"url":null,"abstract":"This research focus on the determination of the numerical solution for the mathematical model of Fokker-Planck equations utilizing a new method, in which Sumudu transformation and homotopy analysis method (SHAM) are used together. By SHAM analytical series solution of any mathematical model including fractional derivative can be obtained. By this method, we constructed the solution of fractional Fokker-Planck equations in Caputo and Caputo-Fabrizio senses. The results show that this method is advantageous and applicable to form the series resolution of the fractional mathematical models.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":"313 4","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Analysis of fractional Fokker-Planck equation with Caputo and Caputo-Fabrizio derivatives\",\"authors\":\"Süleyman Çetinkaya, A. Demir, D. Baleanu\",\"doi\":\"10.52846/ami.v48i1.1473\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This research focus on the determination of the numerical solution for the mathematical model of Fokker-Planck equations utilizing a new method, in which Sumudu transformation and homotopy analysis method (SHAM) are used together. By SHAM analytical series solution of any mathematical model including fractional derivative can be obtained. By this method, we constructed the solution of fractional Fokker-Planck equations in Caputo and Caputo-Fabrizio senses. The results show that this method is advantageous and applicable to form the series resolution of the fractional mathematical models.\",\"PeriodicalId\":43654,\"journal\":{\"name\":\"Annals of the University of Craiova-Mathematics and Computer Science Series\",\"volume\":\"313 4\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of the University of Craiova-Mathematics and Computer Science Series\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.52846/ami.v48i1.1473\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of the University of Craiova-Mathematics and Computer Science Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52846/ami.v48i1.1473","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Analysis of fractional Fokker-Planck equation with Caputo and Caputo-Fabrizio derivatives
This research focus on the determination of the numerical solution for the mathematical model of Fokker-Planck equations utilizing a new method, in which Sumudu transformation and homotopy analysis method (SHAM) are used together. By SHAM analytical series solution of any mathematical model including fractional derivative can be obtained. By this method, we constructed the solution of fractional Fokker-Planck equations in Caputo and Caputo-Fabrizio senses. The results show that this method is advantageous and applicable to form the series resolution of the fractional mathematical models.
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