Fractional Versions of the Fundamental Theorem of Calculus


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.

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

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The authors declare no conflicts of interest.


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