- Turkish Journal of Mathematics and Computer Science
- Vol: 8
- A Truncated $\mathcal{V}$-Fractional Derivative in $\mathbb{R}^n$
A Truncated $\mathcal{V}$-Fractional Derivative in $\mathbb{R}^n$
Authors : José Vanterler Da Costa SOUSA, Edmundo Capelas De OLİVEİRA
Pages : 49-64
View : 5 | Download : 2
Publication Date : 2018-06-30
Article Type : Research
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.Keywords : Truncated $\mathcal{V}$-fractional derivative, multivariable truncated $\mathcal{V}$-fractional derivative, truncated $\mathcal{V}$-fractional partial derivative, truncated $\mathcal{V}$-fractional Jacobian matrix