The paper presents a method for parametric identification of a model of hydrogen thermal desorption from structural materials based on noise-resistant integral measurement processing operators and the theory of conjugate problems of mathematical physics. The special feature of the model is that the time derivative is included not only in the diffusion equation, but also in the nonlinear boundary conditions. In the simplest case, when transformed into an equivalent integro-differential equation, this leads to the emergence of fractional derivatives. In the general terminology of the dynamical systems theory, this is a meaningful example of a memory system. In physical terms: concentrations on the surface and in the bulk ‘remember’ their previous history.