Fractional Versions of the Fundamental Theorem of Calculus

Eliana Contharteze Grigoletto, Edmundo Capelas de Oliveira

Department of Applied Mathematics, University of Campinas, Campinas, Brazil.

DOI: 10.4236/am.2013.47A006                

Abstract

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.

Keywords

Fractional Integral; Fractional Derivative; Riemann-Liouville Derivative; Liouville Derivative; Caputo Derivative; Weyl Derivative and Riesz Derivative

Conflicts of Interest

The authors declare no conflicts of interest.

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