Generalized Taylor's formula for power fractional derivatives
| Autor: | Zitane, Hanaa, Torres, Delfim F. M. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Bol. Soc. Mat. Mex. 29 (2023), no. 3, Paper No. 68, 14pp |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s40590-023-00540-0 |
| Popis: | 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. Comment: This is a preprint of a paper whose final and definite form is published in 'Bolet\'{\i}n de la Sociedad Matem\'{a}tica Mexicana' at [https://www.springer.com/journal/40590] |
| Databáze: | arXiv |
| Externí odkaz: |
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