Fractional Versions of the Fundamental Theorem of Calculus

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.

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.

Cite this paper

E. Grigoletto and E. Oliveira, "Fractional Versions of the Fundamental Theorem of Calculus,"*Applied Mathematics*, Vol. 4 No. 7, 2013, pp. 23-33. doi: 10.4236/am.2013.47A006.

E. Grigoletto and E. Oliveira, "Fractional Versions of the Fundamental Theorem of Calculus,"

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