Restoration of the Initial Data in the Problem for a Diffusion Equation with Fractional Derivative with Respect to Time

Abstract

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 α ∈ (1, 2) with respect to time in a rectangular domain (0, ℓ) × (0, t₀] 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 t₀ .