In this article, the question of the uniqueness of the solution of a time-regular problem for the differential operator equation 𝑙(∙)−𝐴 with the operator is investigated Tricomi 𝐴. The order of the differential expression 𝑙(∙) is considered an arbitrary natural number 𝑛. For the differential expression 𝑙(∙), regular boundary conditions are given for the time variable 𝑡. The operator 𝐴 is generated by the Tricomi equation 𝐴𝑣= 𝑦𝑣𝑥𝑥(𝑥,𝑦) + 𝑣𝑦𝑦(𝑥,𝑦). The boundary conditions for the Tricomi operator are given by the Dirichlet condition on the elliptic part and the fractional derivatives of the solution along the characteristics on the hyperbolic part. It is indicated that this operator is a self-adjoint operator in 𝐿₂(𝛺). The self-adjoint of the operator 𝐴 guarantees the existence of a complete orthonormal system of eigenfunctions in 𝐿₂(𝛺) if 𝛺 is a domain bounded by the Lyapunov curve and the characteristics of the wave equation.