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 and Samarskii-Ionkin type boundary value conditions recording second variable . 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.