{"title":"关于ψ-Hilfer非局部柯西问题的理论","authors":"M. Almalahi, S. K. Panchal","doi":"10.17516/1997-1397-2021-14-2-161-177","DOIUrl":null,"url":null,"abstract":"In this paper, we derive the representation formula of the solution for ψ-Hilfer fractional differential equation with constant coefficient in the form of Mittag-Leffler function by using Picard’s successive approximation. Moreover, by using some properties of Mittag-Leffler function and fixed point theorems such as Banach and Schaefer, we introduce new results of some qualitative properties of solution such as existence and uniqueness. The generalized Gronwall inequality lemma is used in analyze Eα -Ulam-Hyers stability. Finally, one example to illustrate the obtained results","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"On the Theory of ψ-Hilfer Nonlocal Cauchy Problem\",\"authors\":\"M. Almalahi, S. K. Panchal\",\"doi\":\"10.17516/1997-1397-2021-14-2-161-177\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we derive the representation formula of the solution for ψ-Hilfer fractional differential equation with constant coefficient in the form of Mittag-Leffler function by using Picard’s successive approximation. Moreover, by using some properties of Mittag-Leffler function and fixed point theorems such as Banach and Schaefer, we introduce new results of some qualitative properties of solution such as existence and uniqueness. The generalized Gronwall inequality lemma is used in analyze Eα -Ulam-Hyers stability. Finally, one example to illustrate the obtained results\",\"PeriodicalId\":422202,\"journal\":{\"name\":\"Journal of Siberian Federal University. Mathematics and Physics\",\"volume\":\"13 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Siberian Federal University. Mathematics and Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17516/1997-1397-2021-14-2-161-177\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Siberian Federal University. Mathematics and Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17516/1997-1397-2021-14-2-161-177","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we derive the representation formula of the solution for ψ-Hilfer fractional differential equation with constant coefficient in the form of Mittag-Leffler function by using Picard’s successive approximation. Moreover, by using some properties of Mittag-Leffler function and fixed point theorems such as Banach and Schaefer, we introduce new results of some qualitative properties of solution such as existence and uniqueness. The generalized Gronwall inequality lemma is used in analyze Eα -Ulam-Hyers stability. Finally, one example to illustrate the obtained results
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