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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Kummer E., “De integralibus quibusdam definitis et seriebus infinitis”, Journal fur die reine und angewandte Mathematik, 17 (1837), 228–242 | DOI | Zbl

[2] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, V 3 t., v. 1, Gipergeometricheskaya funktsiya. Funktsii Lezhandra, M., 1965

[3] Liouville J., “Memoire sur quelques questions de geometrie et de mecanique, et sur un nouveau genre de calcul pour resoudre ces questions”, J. I'Ecole Roy. Polytechn., 13:21 (1832), 1–69

[4] Riemann B., “Versuch einer allgeimeinen Auffassung der Integration und Differentiation”, Gesammelte Mathematische Werke, Teubner, Leipzig, 1876, 331–344

[5] Kobelev L.Ya., Kobelev Ya.L., “The Fractional Derivatives With Orders as Functions Depending on the Variable of Integration”, Fractional diferentiation and its applications, Proceedings of FDA 04, eds. A. Le Mehauté, J.A. Tenreiro Machado, J. Claude Trigeassou and J. Sabatier, 2005, P. 59–69

[6] Samko S.G., Kilbas A.A., Marichev O.I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Minsk, 1987 | MR