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A note on fractional derivatives and fractional powers of operators. (English) Zbl 1175.26004
A connection between Riemann-Liouville fractional derivatives and fractional powers of positive operators is established and, a discrete version of such derivatives is introduced.

26A33Fractional derivatives and integrals (real functions)
47B65Positive and order bounded operators
Full Text: DOI
[1] Podlubny, I.: Fractional differential equations, (1999) · Zbl 0924.34008
[2] Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives, (1993) · Zbl 0818.26003
[3] Lavoie, J. L.; Osler, T. J.; Tremblay, R.: Fractional derivatives and special functions, SIAM rev. 18, No. 2, 240-268 (1976) · Zbl 0324.44002 · doi:10.1137/1018042
[4] J. Munkhamar, Riemann -- Liouville fractional derivatives and the Taylor -- Riemann series, Uppsala University Department of Mathematics, Project Report, 7, 2004
[5] Ashyralyev, A.; Sobolevskii, P. E.: Well-posedness of parabolic difference equations, (1994) · Zbl 1077.39015
[6] Krein, S. G.: Linear differential equations in Banach space, Transl. math. Monogr. 29 (1971) · Zbl 0236.47034
[7] Tarasov, V. E.: Fractional derivative as fractional power of derivative, Internat. J. Math. 18, 281-299 (2007) · Zbl 1119.26011 · doi:10.1142/S0129167X07004102