Inverse problem for an inhomogeneous fractional equation with the quadrat of pseudoparabolic operator

Abstract

In this paper the issues of unique solvability and construction of a solution of an inverse boundary value problem for an inhomogeneous differential equation containing a quadrat of Hilfer fractional analogue of the pseudoparabolic operator are studied. The spectral problem is studied, eigenvalues and eigenfunctions are found. The solution of the direct and inverse boundary value problems are obtained in the form of Fourier series. Sufficient coefficient conditions for unique solvability of these problems are established. Theorems on absolute and uniform convergence of Fourier series are proved.