Geodesic
The inverse and direct problem for equation of the first kind of convolution on the half-line
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1456-1462.

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In this paper we study the integral equation first kind of convolution on the semi-infinite interval. The next two tasks are: Task is reconstruction of history. From the integral equation it is required to find two functions $u(t)$ for $t>0$ and $f(t)$ for $0$ for given values of the right side of the equation $f(t)$ for $t>b$ ($u(t)$ — solution of integral equation). The problem of inversion of the integral operator. Uniqueness theorems are proved, necessary and sufficient conditions for solvability are found, explicit formulas for solutions are received. 
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A. F. Voronin. The inverse and direct problem for equation of the first kind of convolution on the half-line. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1456-1462. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a101/

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[2] Krein M. G., “Integral equations on the half-line with a kernel depending on the difference of the arguments”, Uspehi Mat. Nauk, 13:5 (1958), 3–120 (Russian) | MR

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[4] F.D. Gahov, Yu.I. Cherskiy, The equations of the áonvolution type, Nauka, M., 1978 (Russian) | MR