Fractional Versions of the Fundamental Theorem of Calculus

By E. C. Grigoletto, E. Capelas de Oliveira. 2013

48 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/7cc34431fe7c3655d32881c766684d67c9acddcf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. D. S. Oliveira
2. E. Capelas de Oliveira
3. J. Sousa
4. Fahd Jarad
5. Thabet Abdeljawad

In Mathematical Physics

1. E. Capelas de Oliveira

In Modeling and Simulation

1. D. S. Oliveira
2. E. Capelas de Oliveira
3. J. Sousa
4. Fahd Jarad

Citations in the corpus

• On a Caputo-type fractional derivative (2018, background): “In this section, we present and prove the fundamental theorem of fractional calculus associated with the generalized fractional integral and the Caputo-type differential operator [3, 5].”