{"title":"具有有界导数的绝对连续函数的Riemann-Liouville分数积分的Ostrowski和梯形不等式","authors":"S. Dragomir","doi":"10.7153/fdc-2020-10-19","DOIUrl":null,"url":null,"abstract":"In this paper we establish some Ostrowski and trapezoid type inequalities for the Riemann-Liouville fractional integrals of absolutely continuous functions with bounded derivatives. Applications for mid-point and trapezoid inequalities are provided as well. They generalize the known results holding for the classical Riemann integral. Some examples for convex functions are also given. Mathematics subject classification (2010): 26D15, 26D10, 26D07, 26A33.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"154 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Ostrowski and trapezoid type inequalities for Riemann-Liouville fractional integrals of absolutely continuous functions with bounded derivatives\",\"authors\":\"S. Dragomir\",\"doi\":\"10.7153/fdc-2020-10-19\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we establish some Ostrowski and trapezoid type inequalities for the Riemann-Liouville fractional integrals of absolutely continuous functions with bounded derivatives. Applications for mid-point and trapezoid inequalities are provided as well. They generalize the known results holding for the classical Riemann integral. Some examples for convex functions are also given. Mathematics subject classification (2010): 26D15, 26D10, 26D07, 26A33.\",\"PeriodicalId\":135809,\"journal\":{\"name\":\"Fractional Differential Calculus\",\"volume\":\"154 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractional Differential Calculus\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/fdc-2020-10-19\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractional Differential Calculus","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/fdc-2020-10-19","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Ostrowski and trapezoid type inequalities for Riemann-Liouville fractional integrals of absolutely continuous functions with bounded derivatives
In this paper we establish some Ostrowski and trapezoid type inequalities for the Riemann-Liouville fractional integrals of absolutely continuous functions with bounded derivatives. Applications for mid-point and trapezoid inequalities are provided as well. They generalize the known results holding for the classical Riemann integral. Some examples for convex functions are also given. Mathematics subject classification (2010): 26D15, 26D10, 26D07, 26A33.