The exact solution of the initial boundary value problem for the equation of anomalous diffusion

Abstract

In this paper, we present an exact solution of the initial boundary value problem of fractional differential equation for anomalous diffusion with Riemann-Liouville time derivative of the order (0, 1), which corresponds to the so-called slow diffusion. A solution over the interval [0, l] is obtained using the Laplaсe transformation and assuming that one of the endpoints (x = 0) is isolated and at the another endpoint (x = l) the constant concentration is kept. The resulting solution is written in fundamental form and represents a generalized power series.