Generalized Taylor's formula for power fractional derivatives
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866913209918685184 |
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| author | Zitane, Hanaa Torres, Delfim F. M. |
| author_facet | Zitane, Hanaa Torres, Delfim F. M. |
| contents | We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version of the classical mean value theorem. We apply our main result to approximate functions in Taylor's expansions at a given point. The explicit interpolation error is also obtained. The new results are illustrated through examples and numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14406 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized Taylor's formula for power fractional derivatives Zitane, Hanaa Torres, Delfim F. M. Spectral Theory 26A24, 26A33, 41A58 We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version of the classical mean value theorem. We apply our main result to approximate functions in Taylor's expansions at a given point. The explicit interpolation error is also obtained. The new results are illustrated through examples and numerical simulations. |
| title | Generalized Taylor's formula for power fractional derivatives |
| topic | Spectral Theory 26A24, 26A33, 41A58 |
| url | https://arxiv.org/abs/2401.14406 |