ABSTRACT
In this paper, we present and prove a new truncated 𝒱 -fractional Taylor’s formula using the truncated 𝒱 -fractional variation of constants formula. In this sense, we present the truncated 𝒱 -fractional Taylor’s remainder by means of 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.
Keywords:
Truncated 𝒱 -fractional derivative; multivariable truncated 𝒱 -fractional derivative; truncated 𝒱 -fractional partial derivative; truncated 𝒱 -fractional Jacobian matrix; truncated 𝒱 -fractional Green’s theorem