Fractional Versions of the Fundamental Theorem of Calculus

• 作者: Edmundo Capelas de Oliveira Eliana Contharteze Grigoletto
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: FRACTIONAL INTEGRAL FRACTIONAL DERIVATIVE Riemann-Liouville DERIVATIVE LIOUVILLE DERIVATIVE Caputo DERIVATIVE WEYL DERIVATIVE and RIESZ DERIVATIVE
• 年，卷（期）: 2013,（7）
• 页码范围: 23-33
• 页数: 11页
• 分类号: O1

摘要

The concept of fractional integral in the Riemann-Liouville, Liouville, Weyl and Riesz sense is presented. Some properties involving the particular Riemann-Liouville integral are mentioned. By means of this concept we present the fractional derivatives, specifically, the Riemann-Liouville, Liouville, Caputo, Weyl and Riesz versions are discussed. The so-called fundamental theorem of fractional calculus is presented and discussed in all these different versions.