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 V-fractional derivative type. In this sense, we propose the derivative of a vector valued function and define the V-fractional Jacobian matrix whose properties allow us to say that: the multivariable truncated V-fractional derivative type, as proposed here, generalizes the truncated V-fractional derivative type and can bee extended to obtain a truncated V-fractional partial derivative type. As applications, we discuss and prove the order change associated with two indices of two truncated V-fractional partial derivative type and propose the truncated V-fractional Green theorem.