Riesz potential operators and inverses via fractional centred derivatives
Fractional centred differences and derivatives definitions are proposed, generalizing to real orders the existing ones valid for even and odd positive integer orders. For each one, suitable integral formulations are obtained. The computations of the involved integrals lead to new generalizations of...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/48391 |
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| _version_ | 1832554341646467072 |
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| author | Manuel Duarte Ortigueira |
| author_facet | Manuel Duarte Ortigueira |
| author_sort | Manuel Duarte Ortigueira |
| collection | DOAJ |
| description | Fractional centred differences and derivatives definitions are
proposed, generalizing to real orders the existing ones valid for
even and odd positive integer orders. For each one, suitable
integral formulations are obtained. The computations of the
involved integrals lead to new generalizations of the Cauchy
integral derivative. To compute this integral, a special
two-straight-line path was used. With this the referred integrals
lead to the well-known Riesz potential operators and their
inverses that emerge as true fractional centred derivatives, but
that can be computed through summations similar to the well-known
Grünwald-Letnikov derivatives. |
| format | Article |
| id | doaj-art-167eb43d4dcf442aaf65652fdaf05380 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-167eb43d4dcf442aaf65652fdaf053802025-02-03T05:51:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/4839148391Riesz potential operators and inverses via fractional centred derivativesManuel Duarte Ortigueira0UNINOVA, Campus da FCT da UNL, Quinta da Torre, Monte de Caparica 2825–114, PortugalFractional centred differences and derivatives definitions are proposed, generalizing to real orders the existing ones valid for even and odd positive integer orders. For each one, suitable integral formulations are obtained. The computations of the involved integrals lead to new generalizations of the Cauchy integral derivative. To compute this integral, a special two-straight-line path was used. With this the referred integrals lead to the well-known Riesz potential operators and their inverses that emerge as true fractional centred derivatives, but that can be computed through summations similar to the well-known Grünwald-Letnikov derivatives.http://dx.doi.org/10.1155/IJMMS/2006/48391 |
| spellingShingle | Manuel Duarte Ortigueira Riesz potential operators and inverses via fractional centred derivatives International Journal of Mathematics and Mathematical Sciences |
| title | Riesz potential operators and inverses via fractional centred
derivatives |
| title_full | Riesz potential operators and inverses via fractional centred
derivatives |
| title_fullStr | Riesz potential operators and inverses via fractional centred
derivatives |
| title_full_unstemmed | Riesz potential operators and inverses via fractional centred
derivatives |
| title_short | Riesz potential operators and inverses via fractional centred
derivatives |
| title_sort | riesz potential operators and inverses via fractional centred derivatives |
| url | http://dx.doi.org/10.1155/IJMMS/2006/48391 |
| work_keys_str_mv | AT manuelduarteortigueira rieszpotentialoperatorsandinversesviafractionalcentredderivatives |