A MIXED PROBLEM FOR A FOURTH ORDER TIME-FRACTIONAL PARTIAL DIFFERENTIAL EQUATION WITH TWO LINES OF DEGENERACY

This article examines an initial-boundary value problem for a fourth-order partial differential equation with a boundary condition violation. By using the method of separation of variables, the problem is reduced to a spectral problem for an ordinary differential equation dependent on the spatial variable. Then, this spectral problem is expressed in an equivalent form as an integral equation with a symmetric kernel. Utilizing the theory of integral equations with symmetric kernels, the eigenvalues, eigenfunctions, and the convergence of the corresponding series are proven. The solution to the problem is constructed as a series in terms of the eigenfunctions of the spectral problem. Necessary conditions for the uniqueness of the solution are determined.