Geodesic
The integral equation with the generalized Mittag--Leffler function in the kernel in the space of integrable functions
Trudy Instituta matematiki, Tome 16 (2008) no. 2, pp. 49-56.

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The integral equation of the first kind containing the generalized Mittag–Leffler function in the kernel is investigated on the half-axis. The necessary and sufficient conditions of a solvability of the considered equation in the weighed space of integrable functions are proved and its solution in closed form is obtained. 
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A. A. Kilbas; N. V. Kniaziuk. The integral equation with the generalized Mittag--Leffler function in the kernel in the space of integrable functions. Trudy Instituta matematiki, Tome 16 (2008) no. 2, pp. 49-56. http://geodesic.mathdoc.fr/item/TIMB_2008_16_2_a4/

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[2] Mittag-Leffler G.M., “Sur larepresentation analytiqie d'ne function monogene”, Acta Math., 29 (1905), 101–181 | DOI | MR

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[5] Kilbas A.A., Knyazyuk N.V., “Svoistva integralnykh operatorov s obobschennoi funktsiei Mittag-Lefflera v yadre”, Vestnik BGU. Ser. 1, 2007, no. 2, 60–64 | MR

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

[7] Kilbas A.A., Knyazyuk N.V., “Integrodifferentsialnoe uravnenie s obobschennoi funktsiei Mittag-Lefflera na poluosi”, Analiticheskie metody analiza i differentsialnykh uravnenii, Tr. 4-i Mezhdunar. konf., posvyaschennoi 100-letiyu akademika F.D. Gakhova (13–19 sentyabrya 2006 g., Minsk, Belarus), T. 1. Matematicheskii analiz, Institut matematiki NAN Belarusi, Minsk, 2006, 57–64

[8] Kilbas A.A., Knyazyuk N.V., “Modifitsirovannye drobnye integraly i proizvodnye na poluosi i differentsialnye uravneniya drobnogo poryadka v prostranstve integriruemykh funktsii”, Trudy Instituta matematiki. Minsk, 15:1 (2007), 68–77