ON THE SOLVABILITY OF THE FIRST INITIAL-BOUNDARY VALUE PROBLEM FOR A ONE-DIMENSIONAL PSEUDOPARABOLIC EQUATION WITH FRACTIONAL DERIVATIVES

Abstract

In the study of inverse problems of mathematical physics, knowledge of the solutions of the corresponding direct (in this case, the first initial boundary value) problem plays an important role. In this paper, we study the existence and uniqueness of the classical solution of the first initial-boundary value problem for a one-dimensional inhomogeneous pseudoparabolic equation with time-fractional Caputo derivatives in a closed rectangle with homogeneous boundary conditions. The existence and uniqueness theorem for the solution of the problem under consideration is proved. The Fourier method is used to prove the existence and uniqueness of a solution to the problem posed. Sufficient conditions are established for the unique solvability of the problem under consideration in the class of continuously differentiable functions. An explicit classical solution of the problem under study is obtained.