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arXiv · 2401.14406

Generalized Taylor's formula for power fractional derivatives

Hanaa Zitane·Delfim F. M. Torres
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Abstract

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.

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BibTeXRIS

Hanaa Zitane, Delfim F. M. Torres. 2023-09-07. Generalized Taylor's formula for power fractional derivatives. https://doi.org/10.1007/s40590-023-00540-0

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