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

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.