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

TL;DR

This paper introduces a new truncated $\

Contribution

It develops a novel truncated $\

Findings

Generalizes the Cauchy-Schwartz inequality.

Provides a new method for error analysis in fractional Taylor approximations.

Derives explicit formulas for $\

Abstract

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.