{"title":"正实轴上Mittag-Leffler函数的积分表示","authors":"E. C. Grigoletto, E. C. Oliveira, R. F. Camargo","doi":"10.5540/TEMA.2019.020.02.217","DOIUrl":null,"url":null,"abstract":"The Mittag-Leffler functions appear in many problems associated with fractional calculus. In this paper, we use the methodology for evaluation of the inverse Laplace transform, proposed by M. N. Berberan-Santos, to show that the three-parameter Mittag-Leffler function has similar integral representations on the positive real axis. Some of the integrals are also presented.","PeriodicalId":163536,"journal":{"name":"TEMA - Tendências em Matemática Aplicada e Computacional","volume":"77 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Integral representations of Mittag-Leffler function on the positive real axis\",\"authors\":\"E. C. Grigoletto, E. C. Oliveira, R. F. Camargo\",\"doi\":\"10.5540/TEMA.2019.020.02.217\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Mittag-Leffler functions appear in many problems associated with fractional calculus. In this paper, we use the methodology for evaluation of the inverse Laplace transform, proposed by M. N. Berberan-Santos, to show that the three-parameter Mittag-Leffler function has similar integral representations on the positive real axis. Some of the integrals are also presented.\",\"PeriodicalId\":163536,\"journal\":{\"name\":\"TEMA - Tendências em Matemática Aplicada e Computacional\",\"volume\":\"77 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"TEMA - Tendências em Matemática Aplicada e Computacional\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5540/TEMA.2019.020.02.217\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"TEMA - Tendências em Matemática Aplicada e Computacional","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5540/TEMA.2019.020.02.217","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
摘要
Mittag-Leffler函数出现在许多与分数阶微积分相关的问题中。在本文中，我们使用M. N. Berberan-Santos提出的求拉普拉斯逆变换的方法来证明三参数Mittag-Leffler函数在正实轴上具有相似的积分表示。文中也给出了一些积分。
Integral representations of Mittag-Leffler function on the positive real axis
The Mittag-Leffler functions appear in many problems associated with fractional calculus. In this paper, we use the methodology for evaluation of the inverse Laplace transform, proposed by M. N. Berberan-Santos, to show that the three-parameter Mittag-Leffler function has similar integral representations on the positive real axis. Some of the integrals are also presented.
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