Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series
New differences of integer orders, which are connected with derivatives of integer orders not approximately, are proposed. These differences are represented by infinite series. A characteristic property of the suggested differences is that its Fourier series transforms have a power-law form. We demo...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2015-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/134842 |
| Summary: | New differences of integer orders, which are connected with derivatives of integer orders not approximately, are proposed. These differences are represented by infinite series. A characteristic property of the suggested differences is that its Fourier series transforms have a power-law form. We demonstrate that the proposed differences of integer orders n are directly connected with the derivatives ∂n/∂xn. In contrast to the usual finite differences of integer orders, the suggested differences give the usual derivatives without approximation. |
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| ISSN: | 2314-4629 2314-4785 |