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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |