On one loaded mixed-type integro-differential equation with fractional Gerasimov--Caputo operators

T. K. Yuldashev ; E. T. Karimov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 211 (2022), pp. 96-113.

Résumé

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.

Détail

Keywords: integro-differential equation, mixed-type equation, degenerate kernel, unique solvability, fractional Gerasimov–Caputo operator.

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