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Revista Brasileira de Ensino de Física

versão impressa ISSN 1806-1117versão On-line ISSN 1806-9126

Resumo

TEODORO, G. Sales; OLIVEIRA, D. S.  e  OLIVEIRA, E. Capelas de. On fractional derivatives. Rev. Bras. Ensino Fís. [online]. 2018, vol.40, n.2, e2307.  Epub 02-Out-2017. ISSN 1806-1117.  http://dx.doi.org/10.1590/1806-9126-rbef-2017-0213.

We present the several ways one can define a fractional derivative, in the form of a historical introduction to fractional calculus. Starting with the concept of fractional derivative, which is a generalization of the Cauchy integral, we approach the fractional derivatives in the senses of Riemann-Liouville and Caputo. We discuss recent proposals of new fractional derivatives which, through an adequate limiting process, recover both the Riemann-Liouville and the Caputo formulations. We also discuss other formulations in which the kernel of the integral is nonsingular. On the basis of a recent criterion, we justify why such derivatives can be considered authentic fractional derivatives. We also present some applications of strictly mathematical nature, together with an application to a specific physical problem.

Palavras-chave : Fractional derivates; Non-integer order calculus; Riemann-Liouville derivative; Caputo derivative; Circuit RL.

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