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Fractional derivative as fractional power of derivative. (English) Zbl 1119.26011
Author’s abstract: Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of selfadjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.

MSC:
26A33 Fractional derivatives and integrals
33C65 Appell, Horn and Lauricella functions
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
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