Nonlocal problem for a fractional-order mixed-type equation with involution

In this paper, we examine the unique solvability of a nonlocal problem for a nonlocal analog of a mixed parabolic-hyperbolic equation with a generalized Riemann–Liouville operator and involution with respect to the space variable. A criterion for the uniqueness of the solution is established and sufficient conditions for the unique solvability of the problem are determined. By the method of separation of variables, a solution is constructed in the form of an absolutely and uniformly convergent series with respect to eigenfunctions of the corresponding one-dimensional spectral problem. The stability of the solution of the problem under consideration under a nonlocal condition is established.