Abstract:
In this paper, boundary-value problems for a third-order mixed differential equation of the parabolic-hyperbolic type with a fractional Gerasimov–Caputo operator are examined. Classes of functions that ensure the unique solvability of the boundary-value problem are found. The existence and uniqueness of a solution of the boundary-value problem are proved.
Keywords:parabolic-hyperbolic equation, Gerasimov–Caputo differential operator, integral equation, uniqueness of solution, existence of solution.