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Fractional Versions of the Fundamental Theorem of Calculus
Department of Applied Mathematics, University of Campinas, Campinas, Brazil
Department of Applied Mathematics, University of Campinas, Campinas, Brazil
- 1 Department of Applied Mathematics, University of Campinas, Campinas, Brazil
- 2 Department of Applied Mathematics, University of Campinas, Campinas, Brazil
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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.
KeywordsFractional IntegralFractional DerivativeRiemann-Liouville DerivativeLiouville DerivativeCaputo DerivativeWeyl Derivative and Riesz Derivative
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