Please use this identifier to cite or link to this item: `http://repositorio.unicamp.br/jspui/handle/REPOSIP/345351`
 Type: Artigo Title: Mittag-Leffler Functions and the Truncated V-fractional Derivative Author: Sousa, J. Vanterler da C.Capelas de Oliveira, E. Abstract: In this paper, we introduce a new type of fractional derivative, which we called truncated V-fractional derivative, for α-differentiable functions, by means of the six-parameter truncated Mittag–Leffler function. One remarkable characteristic of this new derivative is that it generalizes several different fractional derivatives, recently introduced: conformable fractional derivative, alternative fractional derivative, truncated alternative fractional derivative, M-fractional derivative and truncated M-fractional derivative. This new truncated V-fractional derivative satisfies several important properties of the classical derivatives of integer order calculus: linearity, product rule, quotient rule, function composition and the chain rule. Also, as in the case of the Caputo derivative, the derivative of a constant is zero. Since the six parameters Mittag–Leffler function is a generalization of Mittag–Leffler functions of one, two, three, four and five parameters, we were able to extend some of the classical results of the integer-order calculus, namely: Rolle’s theorem, the mean value theorem and its extension. In addition, we present a theorem on the law of exponents for derivatives and as an application we calculate the truncated V-fractional derivative of the two-parameter Mittag–Leffler function. Finally, we present the V-fractional integral from which, as a natural consequence, new results appear as applications. Specifically, we generalize the inverse property, the fundamental theorem of calculus, a theorem associated with classical integration by parts, and the mean value theorem for integrals. We also calculate the V-fractional integral of the two-parameter Mittag–Leffler function. Further, we were able to establish the relation between the truncated V-fractional derivative and the truncated V-fractional integral and the fractional derivative and fractional integral in the Riemann–Liouville sense when the order parameter α lies between 0 and 1 (0 < α < 1) Subject: Mittag-LefflerFunções deRiemann-LiouvilleDerivada fracionária deRiemann-LiouvilleIntegral deMittag-Leffler functionsRiemann-Liouville fractional derivativeRiemann-Liouville integral Country: Suíça Editor: Springer Rights: fechado Identifier DOI: 10.1007/s00009-017-1046-z Address: https://link.springer.com/article/10.1007%2Fs00009-017-1046-z Date Issue: 2017 Appears in Collections: IMECC - Artigos e Outros Documentos

Files in This Item:
File SizeFormat