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Cauchy’s integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order. (English) Zbl 1202.30068
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.

30E99Miscellaneous topics of analysis in the complex domain
26A33Fractional derivatives and integrals (real functions)
Full Text: DOI
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