J. Vanterler da C. SOUSA, E. Capelas de OLİVEİRA

A Truncated V-Fractional Derivative in R n

Using the six parameters truncated Mittag-Leffler function, we introduce a convenient truncatedfunction to define the so-called truncated V-fractional derivative type. In this sense, we propose the derivativeof 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-fractionalderivative type and can be extended to obtain a truncated V-fractional partial derivative type. As applications, wediscuss and prove the order change associated with two indexes of two truncated V-fractional partial derivative typeand propose the truncated V-fractional Green theorem. Finally, we obtain the analytical solution of the V-fractionalheat equation and present a graphical analysis.

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