Geodesic
Fractional type integral operators with Kummer's confluent hypergeometric function in the kernel
Trudy Instituta matematiki, Tome 19 (2011) no. 1, pp. 22-31

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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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     author = {A. P. Grinko},
     title = {Fractional type integral operators with {Kummer's} confluent hypergeometric function in the kernel},
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A. P. Grinko. Fractional type integral operators with Kummer's confluent hypergeometric function in the kernel. Trudy Instituta matematiki, Tome 19 (2011) no. 1, pp. 22-31. http://geodesic.mathdoc.fr/item/TIMB_2011_19_1_a2/