AN INVERSE PROBLEM FOR A FRACTIONAL PARABOLIC EQUATION WITH INVOLUTION (Scientific journal of the Fergana State University, 2023)
In this paper, we consider an inverse problem for a fourth-order fractional parabolic equation with a fractional Caputo operator and involution. Using the method of separation of variables, the solution to the problem is constructed in the form of a Fourier series. Theorems on the existence and uniqueness of a solution to the considered problem are proved. A criterion for the existence and uniqueness of a regular solution of the problem in a given domain is established.Obtained results can be used in the study of boundary value problems for partial differential equations of fractional order, as well as in the theory of equations of mathematical physics.