Fractional definite integral

Manuel Ortigueira; José Machado

doi:10.3390/fractalfract1010002

Fractional definite integral

Manuel Ortigueira, José Machado

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

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 and R³ are also proposed.

Original language	English
Article number	2
Pages (from-to)	1-9
Number of pages	9
Journal	Fractal and Fractional
Volume	1
Issue number	1
DOIs	https://doi.org/10.3390/fractalfract1010002
Publication status	Published - Dec 2017

Keywords

Definite fractional integral
Fractional derivative
Fractional integral

Access to Document

10.3390/fractalfract1010002

Cite this

@article{8a96123cb2e641e08c66a64dca5b9a53,

title = "Fractional definite integral",

abstract = "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 and R3 are also proposed.",

keywords = "Definite fractional integral, Fractional derivative, Fractional integral",

author = "Manuel Ortigueira and Jos{\'e} Machado",

year = "2017",

month = dec,

doi = "10.3390/fractalfract1010002",

language = "English",

volume = "1",

pages = "1--9",

journal = "Fractal and Fractional",

issn = "2504-3110",

publisher = "MDPI AG",

number = "1",

}

TY - JOUR

T1 - Fractional definite integral

AU - Ortigueira, Manuel

AU - Machado, José

PY - 2017/12

Y1 - 2017/12

N2 - 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 and R3 are also proposed.

AB - 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 and R3 are also proposed.

KW - Definite fractional integral

KW - Fractional derivative

KW - Fractional integral

UR - http://www.scopus.com/inward/record.url?scp=85052579709&partnerID=8YFLogxK

U2 - 10.3390/fractalfract1010002

DO - 10.3390/fractalfract1010002

M3 - Article

AN - SCOPUS:85052579709

SN - 2504-3110

VL - 1

SP - 1

EP - 9

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 1

M1 - 2

ER -

Fractional definite integral

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this