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Zbl 1202.30068
Jumarie, Guy
Cauchy's integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order. (English)
[J] Appl. Math. Lett. 23, No. 12, 1444-1450 (2010). ISSN 0893-9659

Summary: The modified Riemann-Liouville fractional derivative applies to functions which are fractional differentiable but not differentiable, in such a manner that they cannot be analyzed by means of the Djrbashian fractional derivative. It provides a fractional Taylor series for functions which are infinitely fractional differentiable, and this result suggests to introduce a definition of analytic functions of fractional order. Cauchy's conditions for fractional differentiability in the complex plane and the Cauchy integral formula are derived for these kinds of functions.

MSC 2000:: *30E99 Miscellaneous topics of analysis in the complex domain
26A33 Fractional derivatives and integrals (real functions)

Keywords: fractional derivative; fractional Taylor series; Mittag-Leffler function; Cauchy integral formula

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Zentralblatt MATH Berlin [Germany]