RESTORATION OF THE INITIAL DATA IN THE PROBLEM FOR A DIFFUSION EQUATION WITH FRACTIONAL DERIVATIVE WITH RESPECT TO TIME

摘要

We prove the correctness of the inverse problem of finding a pair of functions: the classical solution u(x,t) of the first boundary-value problem for a linear diffusion equation with regularized fractional derivative of order a €(1,2) with respect to time in a rectangular domain (0,ℓ)×(0,t_0] and unknown initial values of the function u(x,t) for the case of additionally given values of the function at a certain fixed time t_0.