Fractional Definite Integral
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2017-07-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/1/1/2 |
| _version_ | 1818645707718918144 |
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| author | Manuel Ortigueira José Machado |
| author_facet | Manuel Ortigueira José Machado |
| author_sort | Manuel Ortigueira |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T00:35:02Z |
| format | Article |
| id | doaj.art-709c291ee95e4dcc8243cd0f9ee162d4 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-12-17T00:35:02Z |
| publishDate | 2017-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-709c291ee95e4dcc8243cd0f9ee162d42022-12-21T22:10:10ZengMDPI AGFractal and Fractional2504-31102017-07-0111210.3390/fractalfract1010002fractalfract1010002Fractional Definite IntegralManuel Ortigueira0José Machado1UNINOVA and DEE of Faculdade de Ciências e Tecnologia da UNL, Campus da FCT da UNL, Quinta da Torre, 2829–516 Caparica, PortugalDepartment of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249–015 Porto, Portugal; e-mail: <email>jtm@isep.ipp.pt</email>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.https://www.mdpi.com/2504-3110/1/1/2fractional integralfractional derivativedefinite fractional integral |
| spellingShingle | Manuel Ortigueira José Machado Fractional Definite Integral Fractal and Fractional fractional integral fractional derivative definite fractional integral |
| title | Fractional Definite Integral |
| title_full | Fractional Definite Integral |
| title_fullStr | Fractional Definite Integral |
| title_full_unstemmed | Fractional Definite Integral |
| title_short | Fractional Definite Integral |
| title_sort | fractional definite integral |
| topic | fractional integral fractional derivative definite fractional integral |
| url | https://www.mdpi.com/2504-3110/1/1/2 |
| work_keys_str_mv | AT manuelortigueira fractionaldefiniteintegral AT josemachado fractionaldefiniteintegral |