A Truncated $\mathcal{V}$-Fractional Derivative in $\mathbb{R}^n$

Authors : José Vanterler Da Costa SOUSA, Edmundo Capelas De OLİVEİRA

Pages : 49-64

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Publication Date : 2018-06-30

Article Type : Research Paper

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