×

zbMATH — the first resource for mathematics

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.

MSC:
26A33 Fractional derivatives and integrals
47B65 Positive linear operators and order-bounded operators
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Podlubny, I., Fractional differential equations, (1999), Academic Press New York · Zbl 0918.34010
[2] Samko, S.G.; Kilbas, A.A.; Marichev, O.I., Fractional integrals and derivatives, (1993), Gordon and Breach Science Publishers London · Zbl 0818.26003
[3] Lavoie, J.L.; Osler, T.J.; Tremblay, R., Fractional derivatives and special functions, SIAM rev., 18, 2, 240-268, (1976) · Zbl 0324.44002
[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), Birkhäuser Verlag Basel, Boston, Berlin · Zbl 1077.39015
[6] Krein, S.G., Linear differential equations in Banach space, Transl. math. monogr., vol. 29, (1971), Amer. Math. Soc. · Zbl 0636.34056
[7] Tarasov, V.E., Fractional derivative as fractional power of derivative, Internat. J. math., 18, 281-299, (2007) · Zbl 1119.26011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.