{"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}
引用次数: 3
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.
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