TITLE:
Fractional Versions of the Fundamental Theorem of Calculus
AUTHORS:
Eliana Contharteze Grigoletto, Edmundo Capelas de Oliveira
KEYWORDS:
Fractional Integral; Fractional Derivative; Riemann-Liouville Derivative; Liouville Derivative; Caputo Derivative; Weyl Derivative and Riesz Derivative
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.7A,
July
8,
2013
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.