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Fractal and Fractional
Open AccessArticle

Fractional Definite Integral

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UNINOVA and DEE of Faculdade de Ciências e Tecnologia da UNL, Campus da FCT da UNL, Quinta da Torre, 2829–516 Caparica, Portugal
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INESC-ID, Rua Alves Redol, 9, 1000–029 Lisboa, Portugal
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Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249–015 Porto, Portugal; e-mail: [email protected]
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Author to whom correspondence should be addressed.
Fractal Fract 2017, 1(1), 2; https://doi.org/10.3390/fractalfract1010002
Received: 14 June 2017 / Revised: 30 June 2017 / Accepted: 30 June 2017 / Published: 2 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
MDPI and ACS Style

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

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