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 Tr. Inst. Mat., 2011, Volume 19, Number 1, Pages 22–31 (Mi timb136)

Fractional type integral operators with Kummer's confluent hypergeometric function in the kernel

A. P. Grinko

A. S. Pushkin Brest State University

Abstract: The properties of the fractional type integral operator with Kummer's confluent hypergeometric function in the kernel are studied. Composition formula and explicit form of the inverse integral operator are obtained. The latter generalizes fractional derivatives of Riemann–Liouville and Marchaud type. New integral representation of confluent Kummer's hypergeometric function is proved.

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UDC: 517.444

Citation: A. P. Grinko, “Fractional type integral operators with Kummer's confluent hypergeometric function in the kernel”, Tr. Inst. Mat., 19:1 (2011), 22–31

Citation in format AMSBIB
\Bibitem{Gri11} \by A.~P.~Grinko \paper Fractional type integral operators with Kummer's confluent hypergeometric function in the kernel \jour Tr. Inst. Mat. \yr 2011 \vol 19 \issue 1 \pages 22--31 \mathnet{http://mi.mathnet.ru/timb136}