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Generalized Taylor’s formula for power fractional derivatives by Hanaa Zitane; Delfim F. M. Torres is a Mathematics article available to read on EtoBox.

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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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Author

Hanaa Zitane; Delfim F. M. Torres

Publisher

Springer Science and Business Media LLC

Published

2023

Language

EN

Field

Mathematics (Physical Sciences)