Abstract:
This article is devoted to study the boundary value problems of the first and second kind with respect
to the spatial variable for a mixed inhomogeneous differential equation of parabolic-hyperbolic type with
a fractional Caputo operator in a rectangular domain. In the study of such boundary value problems, we
abandoned the boundary value condition with respect to the first argument and instead it is used additional
gluing condition. In this case, in the justification of the unique solvability of the problems, the conditions
on the boundary domain are removed. This allowed us to weaken the criterion for the unique solvability of
boundary value problems under consideration. The solution is constructed in the form of Fourier series with
eigenfunctions corresponding to homogeneous spectral problems. Estimates for the convergence of Fourier
series are obtained as a regular solution of this mixed equation.
