{"title":"广义Riemann - Liouville算子的积分拉普拉斯变换反演","authors":"I. I. Bavrin, O. Yaremko","doi":"10.13108/2016-8-3-41","DOIUrl":null,"url":null,"abstract":"We employ the integral Laplace transform to invert the generalized RiemannLiouville operator in a closed form. We establish that the inverse generalized RiemannLiouville operator is a differential or integral-differential operator. We establish a relation between Riemann-Liouville operator and Temlyakov-Bavrin operator. We provide new examples of generalized Riemann-Liouville operator.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"19 1","pages":"41-48"},"PeriodicalIF":0.5000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inverting of generalized Riemann - Liouville operator by means of integral Laplace transform\",\"authors\":\"I. I. Bavrin, O. Yaremko\",\"doi\":\"10.13108/2016-8-3-41\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We employ the integral Laplace transform to invert the generalized RiemannLiouville operator in a closed form. We establish that the inverse generalized RiemannLiouville operator is a differential or integral-differential operator. We establish a relation between Riemann-Liouville operator and Temlyakov-Bavrin operator. We provide new examples of generalized Riemann-Liouville operator.\",\"PeriodicalId\":43644,\"journal\":{\"name\":\"Ufa Mathematical Journal\",\"volume\":\"19 1\",\"pages\":\"41-48\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2016-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ufa Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.13108/2016-8-3-41\",\"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":"Ufa Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13108/2016-8-3-41","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Inverting of generalized Riemann - Liouville operator by means of integral Laplace transform
We employ the integral Laplace transform to invert the generalized RiemannLiouville operator in a closed form. We establish that the inverse generalized RiemannLiouville operator is a differential or integral-differential operator. We establish a relation between Riemann-Liouville operator and Temlyakov-Bavrin operator. We provide new examples of generalized Riemann-Liouville operator.
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