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Fractal Fract 2017, 1(1), 2;

Fractional Definite Integral

UNINOVA and DEE of Faculdade de Ciências e Tecnologia da UNL, Campus da FCT da UNL, Quinta da Torre, 2829–516 Caparica, Portugal
INESC-ID, Rua Alves Redol, 9, 1000–029 Lisboa, Portugal
Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249–015 Porto, Portugal; e-mail:
Author to whom correspondence should be addressed.
Received: 14 June 2017 / Revised: 30 June 2017 / Accepted: 30 June 2017 / Published: 2 July 2017
Full-Text   |   PDF [236 KB, uploaded 25 July 2017]


This paper proposes the definition of fractional definite integral and analyses the corresponding fundamental theorem of fractional calculus. In this context, we studied the relevant properties of the fractional derivatives that lead to such a definition. Finally, integrals on R2 R 2 and R3 R 3 are also proposed. View Full-Text
Keywords: fractional integral; fractional derivative; definite fractional integral fractional integral; fractional derivative; definite fractional integral
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Ortigueira, M.; Machado, J. Fractional Definite Integral. Fractal Fract 2017, 1, 2.

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