Generalized Taylor's formula for power fractional derivatives

Fuente: arXiv
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Main Authors: Zitane, Hanaa, Torres, Delfim F. M.
Format: Preprint
Published: 2023
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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