{"title":"奇异分数阶微分方程的一个新问题","authors":"Amele Taieb, Z. Dahmani","doi":"10.1080/1726037X.2016.1250502","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we introduce a new class of nonlinear singular fractional differential equations. We axe interested in the singularity by using the contraction mapping principle and Schauder fixed point theorem. We present new results on the existence and uniqueness of solutions. Moreover, we investigate the Ulam-Hyers stability and the generalized Ulam-Hyers stability for this fractional equations. Some examples are provided to illustrate the application of our results.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"14 1","pages":"165 - 187"},"PeriodicalIF":0.4000,"publicationDate":"2016-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2016.1250502","citationCount":"14","resultStr":"{\"title\":\"A new problem of singular fractional differential equations\",\"authors\":\"Amele Taieb, Z. Dahmani\",\"doi\":\"10.1080/1726037X.2016.1250502\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we introduce a new class of nonlinear singular fractional differential equations. We axe interested in the singularity by using the contraction mapping principle and Schauder fixed point theorem. We present new results on the existence and uniqueness of solutions. Moreover, we investigate the Ulam-Hyers stability and the generalized Ulam-Hyers stability for this fractional equations. Some examples are provided to illustrate the application of our results.\",\"PeriodicalId\":42788,\"journal\":{\"name\":\"Journal of Dynamical Systems and Geometric Theories\",\"volume\":\"14 1\",\"pages\":\"165 - 187\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2016-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/1726037X.2016.1250502\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamical Systems and Geometric Theories\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/1726037X.2016.1250502\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamical Systems and Geometric Theories","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/1726037X.2016.1250502","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
A new problem of singular fractional differential equations
Abstract In this paper, we introduce a new class of nonlinear singular fractional differential equations. We axe interested in the singularity by using the contraction mapping principle and Schauder fixed point theorem. We present new results on the existence and uniqueness of solutions. Moreover, we investigate the Ulam-Hyers stability and the generalized Ulam-Hyers stability for this fractional equations. Some examples are provided to illustrate the application of our results.
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