Geodesic
On one loaded mixed-type integro-differential equation with fractional Gerasimov--Caputo operators
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 211 (2022), pp. 96-113

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In this paper, we examine the unique solvability of a boundary-value problem for a loaded mixed-type integro-differential equation with fractional Gerasimov–Caputo operators, spectral parameters, and small coefficients of mixed derivatives. The solution of the problem is obtained in the form of a Fourier series. The unique solvability of the problem for regular values of the spectral parameters is proved. The continuous dependence of the solution of the boundary-value problem on small parameters and on given functions is studied for regular values of the spectral parameters.
Keywords: integro-differential equation, mixed-type equation, degenerate kernel, unique solvability, fractional Gerasimov–Caputo operator. 
@article{INTO_2022_211_a6,
     author = {T. K. Yuldashev and E. T. Karimov},
     title = {On one loaded mixed-type integro-differential equation with fractional {Gerasimov--Caputo} operators},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {96--113},
     publisher = {mathdoc},
     volume = {211},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_211_a6/}
}
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T. K. Yuldashev; E. T. Karimov. On one loaded mixed-type integro-differential equation with fractional Gerasimov--Caputo operators. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 211 (2022), pp. 96-113. http://geodesic.mathdoc.fr/item/INTO_2022_211_a6/