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arXiv 1707.020072017-07-07math.CA

Truncated $\mathcal{V}$-fractional Taylor's formula with applications

J. Vanterler da C. Sousa, E. Capelas de Oliveira

备注：: 22 pages

英文摘要：

In this paper, we present and prove a new truncated $\mathcal{V}$-fractional Taylor's formula using the truncated $\mathcal{V}$-fractional variation of constants formula. In this sense, we present the truncated $\mathcal{V}$-fractional Taylor's remainder by means of $\mathcal{V}$-fractional integral, essential for analyzing and comparing the error, when approaching functions by polynomials. From these new results, some applications were made involving some inequalities, specifically, we generalize the Cauchy-Schwartz inequality.

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