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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     author = {A. A. Kilbas and N. V. Kniaziuk},
     title = {The integral equation with the generalized {Mittag--Leffler} function in the kernel in the space of integrable functions},
     journal = {Trudy Instituta matematiki},
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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/