Samarskii-Ionkin two-point boundary conditions for a fractional pseudoparabolic equation

This paper is devoted to study the mixed problem for a nonhomogeneous pseudoparabolic equation. The Hilfer fractional equation is studied with initial value conditions recording first variable t and Samarskii-Ionkin type boundary value conditions recording second variable x. Spectral problem is studied and eigenvalues, eigenfunctions are found. The solution is constructed on the form of Fourier series. Existence and uniqueness of solution's theorems are proved.