Title: A truncated $\mathcal{V}$-fractional derivative in $\mathbb{R}^n$,
Abstract: Using the six parameters truncated Mittag-Leffler function, we introduce a
convenient truncated function to define the so-called truncated
$\mathcal{V}$-fractional derivative type. After a discussion involving some
properties associated with this derivative, we propose the derivative of a
vector valued function and define the $\mathcal{V}$-fractional Jacobian matrix
whose properties allow us to say that: the multivariable truncated
$\mathcal{V}$-fractional derivative type, as proposed here, generalizes the
truncated $\mathcal{V}$-fractional derivative type and can bee extended to
obtain a truncated $\mathcal{V}$-fractional partial derivative type. As
applications we discuss and prove the change of order associated with two index
i.e., the commutativity of two truncated $\mathcal{V}$-fractional partial
derivative type and propose the truncated $\mathcal{V}$-fractional Green's
theorem.